Log in

Relevant bibliographies by topics / Zeros of zeta function / Journal articles

To see the other types of publications on this topic, follow the link: Zeros of zeta function.

Journal articles on the topic 'Zeros of zeta function'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Zeros of zeta function.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Garunkštis, Ramūnas, and Joern Steuding. "QUESTIONS AROUND THE NONTRIVIAL ZEROS OF THE RIEMANN ZETA-FUNCTION. COMPUTATIONS AND CLASSIFICATIONS." Mathematical Modelling and Analysis 16, no. 1 (2011): 72–81. http://dx.doi.org/10.3846/13926292.2011.560616.

Full text

Abstract:

We study the sequence of nontrivial zeros of the Riemann zeta-function with respect to sequences of zeros of other related functions, namely, the Hurwitz zeta-function and the derivative of Riemann's zeta-function. Finally, we investigate connections of the nontrivial zeros with the periodic zeta-function. On the basis of computation we derive several classifications of the nontrivial zeros of the Riemann zeta-function and stateproblems which mightbe ofinterestfor abetter understanding of the distribution of those zeros.

APA, Harvard, Vancouver, ISO, and other styles

2

Sekatskii, Sergey. "On the Sums over Inverse Powers of Zeros of the Hurwitz Zeta Function and Some Related Properties of These Zeros." Symmetry 16, no. 3 (2024): 326. http://dx.doi.org/10.3390/sym16030326.

Full text

Abstract:

Recently, we have applied the generalized Littlewood theorem concerning contour integrals of the logarithm of the analytical function to find the sums over inverse powers of zeros for the incomplete gamma and Riemann zeta functions, polygamma functions, and elliptical functions. Here, the same theorem is applied to study such sums for the zeros of the Hurwitz zeta function ζ(s,z), including the sum over the inverse first power of its appropriately defined non-trivial zeros. We also study some related properties of the Hurwitz zeta function zeros. In particular, we show that, for any natural N

APA, Harvard, Vancouver, ISO, and other styles

3

HASSEN, ABDUL, and HIEU D. NGUYEN. "A ZERO-FREE REGION FOR HYPERGEOMETRIC ZETA FUNCTIONS." International Journal of Number Theory 07, no. 04 (2011): 1033–43. http://dx.doi.org/10.1142/s1793042111004678.

Full text

Abstract:

This paper investigates the location of "trivial" zeros of some hypergeometric zeta functions. Analogous to Riemann's zeta function, we demonstrate that they possess a zero-free region on a left-half complex plane, except for infinitely many zeros regularly spaced on the negative real axis.

APA, Harvard, Vancouver, ISO, and other styles

4

Cox, Darrell. "Companion Riemann Zeta Function Zeros." Global Journal of Pure and Applied Mathematics 20, no. 3 (2024): 617–41. https://doi.org/10.37622/gjpam/20.3.2024.617-641.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Bayer, Pilar. "La hipòtesi de Riemann: El gran repte pendent." Mètode Revista de difusió de la investigació, no. 8 (June 5, 2018): 35. http://dx.doi.org/10.7203/metode.0.8903.

Full text

Abstract:

The Riemann hypothesis is an unproven statement referring to the zeros of the Riemann zeta function. Bernhard Riemann calculated the first six non-trivial zeros of the function and observed that they were all on the same straight line. In a report published in 1859, Riemann stated that this might very well be a general fact. The Riemann hypothesis claims that all non-trivial zeros of the zeta function are on the the line x = 1/2. The more than ten billion zeroes calculated to date, all of them lying on the critical line, coincide with Riemann’s suspicion, but no one has yet been able to prove

APA, Harvard, Vancouver, ISO, and other styles

6

Pushkarev, Petr. "Constant quality of the Riemann zeta's non-trivial zeros." Global Journal of Pure and Applied Mathematics 13, no. 6 (2017): 1987–92. https://doi.org/10.5281/zenodo.822059.

Full text

Abstract:

In this article we are closely examining Riemann zeta function's non-trivial zeros. Especially, we examine real part of non-trivial zeros. Real part of Riemann zeta function's non-trivial zeros is considered in the light of constant quality of such zeros. We propose and prove a theorem of this quality. We also uncover a definition phenomenons of zeta and Riemann xi functions. In conclusion and as an conclusion we observe Riemann hypothesis in perspective of our researches.

APA, Harvard, Vancouver, ISO, and other styles

7

SUZUKI, MASATOSHI. "A RELATION BETWEEN THE ZEROS OF TWO DIFFERENT L-FUNCTIONS WHICH HAVE AN EULER PRODUCT AND FUNCTIONAL EQUATION." International Journal of Number Theory 01, no. 03 (2005): 401–29. http://dx.doi.org/10.1142/s1793042105000248.

Full text

Abstract:

As automorphic L-functions or Artin L-functions, several classes of L-functions have Euler products and functional equations. In this paper we study the zeros of L-functions which have Euler products and functional equations. We show that there exists a relation between the zeros of the Riemann zeta-function and the zeros of such L-functions. As a special case of our results, we find relations between the zeros of the Riemann zeta-function and the zeros of automorphic L-functions attached to elliptic modular forms or the zeros of Rankin–Selberg L-functions attached to two elliptic modular form

APA, Harvard, Vancouver, ISO, and other styles

8

Bialas, P., Z. Burda, and D. A. Johnston. "Partition function zeros of zeta-urns." Condensed Matter Physics 27, no. 3 (2024): 33601. http://dx.doi.org/10.5488/cmp.27.33601.

Full text

Abstract:

We discuss the distribution of partition function zeros for the grand-canonical ensemble of the zeta-urn model, where tuning a single parameter can give a first or any higher order condensation transition. We compute the locus of zeros for finite-size systems and test scaling relations describing the accumulation of zeros near the critical point against theoretical predictions for both the first and higher order transition regimes.

APA, Harvard, Vancouver, ISO, and other styles

9

DUBICKAS, A., R. GARUNKŠTIS, J. STEUDING, and R. STEUDING. "ZEROS OF THE ESTERMANN ZETA FUNCTION." Journal of the Australian Mathematical Society 94, no. 1 (2013): 38–49. http://dx.doi.org/10.1017/s1446788712000419.

Full text

Abstract:

AbstractIn this paper we investigate the zeros of the Estermann zeta function $E(s; k/ \ell , \alpha )= { \mathop{\sum }\nolimits}_{n= 1}^{\infty } {\sigma }_{\alpha } (n) \exp (2\pi ink/ \ell ){n}^{- s} $ as a function of a complex variable $s$, where $k$ and $\ell $ are coprime integers and ${\sigma }_{\alpha } (n)= {\mathop{\sum }\nolimits}_{d\vert n} {d}^{\alpha } $ is the generalized divisor function with a fixed complex number $\alpha $. In particular, we study the question on how the zeros of $E(s; k/ \ell , \alpha )$ depend on the parameters $k/ \ell $ and $\alpha $. It turns out that

APA, Harvard, Vancouver, ISO, and other styles

10

Nakai, Keita. "Discrete universality theorem for Matsumoto zeta-functions and nontrivial zeros of the Riemann zeta-function." Mathematical Modelling and Analysis 30, no. 1 (2025): 97–108. https://doi.org/10.3846/mma.2025.20817.

Full text

Abstract:

In 2017, Garunkštis, Laurinčikas and Macaitienė proved the discrete universality theorem for the Riemann zeta-function shifted by imaginary parts of nontrivial zeros of the Riemann zeta-function. This discrete universality has been extended to various zeta-functions and L-functions. In this paper, we generalize this discrete universality for Matsumoto zeta-functions.

APA, Harvard, Vancouver, ISO, and other styles

11

LeClair, André. "Riemann Hypothesis and Random Walks: The Zeta Case." Symmetry 13, no. 11 (2021): 2014. http://dx.doi.org/10.3390/sym13112014.

Full text

Abstract:

In previous work, it was shown that if certain series based on sums over primes of non-principal Dirichlet characters have a conjectured random walk behavior, then the Euler product formula for its L-function is valid to the right of the critical line ℜ(s)>12, and the Riemann hypothesis for this class of L-functions follows. Building on this work, here we propose how to extend this line of reasoning to the Riemann zeta function and other principal Dirichlet L-functions. We apply these results to the study of the argument of the zeta function. In another application, we define and study a on

APA, Harvard, Vancouver, ISO, and other styles

12

MENEZES, G., B. F. SVAITER, and N. F. SVAITER. "RIEMANN ZETA ZEROS AND PRIME NUMBER SPECTRA IN QUANTUM FIELD THEORY." International Journal of Modern Physics A 28, no. 26 (2013): 1350128. http://dx.doi.org/10.1142/s0217751x13501285.

Full text

Abstract:

The Riemann hypothesis states that all nontrivial zeros of the zeta function lie in the critical line Re (s) = 1/2. Hilbert and Pólya suggested that one possible way to prove the Riemann hypothesis is to interpret the nontrivial zeros in the light of spectral theory. Using the construction of the so-called super-zeta functions or secondary zeta functions built over the Riemann nontrivial zeros and the regularity property of one of this function at the origin, we show that it is possible to extend the Hilbert–Pólya conjecture to systems with countably infinite number of degrees of freedom. The

APA, Harvard, Vancouver, ISO, and other styles

13

Dueñas, J. G., and N. F. Svaiter. "Riemann zeta zeros and zero-point energy." International Journal of Modern Physics A 29, no. 09 (2014): 1450051. http://dx.doi.org/10.1142/s0217751x14500511.

Full text

Abstract:

The sequence of nontrivial zeros of the Riemann zeta function is zeta regularizable. Therefore, systems with countably infinite number of degrees of freedom described by self-adjoint operators whose spectra is given by this sequence admit a functional integral formulation. We discuss the consequences of the existence of such self-adjoint operators in field theory framework. We assume that they act on a massive scalar field coupled to a background field in a (d+1)-dimensional flat space–time where the scalar field is confined to the interval [0, a] in one of its dimensions and there are no rest

APA, Harvard, Vancouver, ISO, and other styles

14

Cox, Darrell. "The Prime Number Theorem, Riemann Zeta Function Zeros, and Dynamical Zeta Functions." Global Journal of Pure and Applied Mathematics 21, no. 1 (2025): 15–34. https://doi.org/10.37622/gjpam/21.1.2025.15-34.

Full text

APA, Harvard, Vancouver, ISO, and other styles

15

Alhadbani, Ahlam, and Stromberg Fredrik. "The Riemann Zeta Function and Its Analytic Continuation." British Journal of Mathematics & Computer Science 22, no. 5 (2017): 1–47. https://doi.org/10.9734/BJMCS/2017/32796.

Full text

Abstract:

The objective of this dissertation is to study the Riemann zeta function in particular it will examine its analytic continuation, functional equation and applications. We will begin with some historical background, then define of the zeta function and some important tools which lead to the functional equation. We will present four different proofs of the functional equation. In addition, the (s) has generalizations, and one of these the Dirichlet L-function will be presented. Finally, the zeros of (s) will be studied.

APA, Harvard, Vancouver, ISO, and other styles

16

Maples, Kenneth, and Brad Rodgers. "Bootstrapped zero density estimates and a central limit theorem for the zeros of the zeta function." International Journal of Number Theory 11, no. 07 (2015): 2087–107. http://dx.doi.org/10.1142/s1793042115500918.

Full text

Abstract:

We unconditionally prove a central limit theorem for linear statistics of the zeros of the Riemann zeta function with diverging variance. Previously, theorems of this sort have been proved under the assumption of the Riemann hypothesis. The result mirrors central limit theorems in random matrix theory that have been proved by Szegő, Spohn, and Soshnikov among others, and therefore provides support for the view that the zeros of the zeta function are distributed like the eigenvalues of a random matrix. A key ingredient in our proof is a simple bootstrapping of classical zero density estimates o

APA, Harvard, Vancouver, ISO, and other styles

17

Lam Kai, Shun. "A Verification of Riemann Non-Trivial Zeros by Complex Analysis by Matlab™ Computation." European Journal of Statistics and Probability 11, no. 1 (2023): 69–83. http://dx.doi.org/10.37745/ejsp.2013/vol11n16983.

Full text

Abstract:

With my most recent paper, I tried to prove the Riemann Hypothesis by catching out those contradictory parts of the non-trivial zeros. In the present paper, I will try to verify these known values of Riemann nontrivial zeros by first using U.S.A. Matlab coding with a list of well-organized complex analysis theories. At the same time, as the major core of my verification is just a mono-direction one (i.e. there may be a possibility of the missing non-trivial zeros although the residue value is zero), hence this author try to solve such problem by assuming that there are some other zeros existin

APA, Harvard, Vancouver, ISO, and other styles

18

Lagarias, Jeffrey C., and Brad Rodgers. "HIGHER CORRELATIONS AND THE ALTERNATIVE HYPOTHESIS." Quarterly Journal of Mathematics 71, no. 1 (2020): 257–80. http://dx.doi.org/10.1093/qmathj/haz043.

Full text

Abstract:

Abstract The Alternative Hypothesis (AH) concerns a hypothetical and unlikely picture of how zeros of the Riemann zeta function are spaced, which one would like to rule out. In the Alternative Hypothesis, the renormalized distance between non-trivial zeros is supposed to always lie at a half integer. It is known that the Alternative Hypothesis is compatible with what is known about the pair correlation function of zeta zeros. We ask whether what is currently known about higher correlation functions of the zeros is sufficient to rule out the Alternative Hypothesis and show by construction of an

APA, Harvard, Vancouver, ISO, and other styles

19

FARAG, HANY M. "DIRICHLET TRUNCATIONS OF THE RIEMANN ZETA FUNCTION IN THE CRITICAL STRIP POSSESS ZEROS NEAR EVERY VERTICAL LINE." International Journal of Number Theory 04, no. 04 (2008): 653–62. http://dx.doi.org/10.1142/s1793042108001596.

Full text

Abstract:

We study the zeros of the finite truncations of the alternating Dirichlet series expansion of the Riemann zeta function in the critical strip. We do this with an (admittedly highly) ambitious goal in mind. Namely, that this series converges to the zeta function (up to a trivial term) in the critical strip and our hope is that if we can obtain good estimates for the zeros of these approximations it may be possible to generalize some of the results to zeta itself. This paper is a first step towards this goal. Our results show that these finite approximations have zeros near every vertical line (

APA, Harvard, Vancouver, ISO, and other styles

20

McPhedran, Ross C., Lindsay C. Botten, and Nicolae-Alexandru P. Nicorovici. "Null trajectories for the symmetrized Hurwitz zeta function." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2077 (2006): 303–19. http://dx.doi.org/10.1098/rspa.2006.1763.

Full text

Abstract:

We consider the Hurwitz zeta function ζ ( s , a ) and develop asymptotic results for a = p / q , with q large, and, in particular, for p / q tending to 1/2. We also study the properties of lines along which the symmetrized parts of ζ ( s , a ), ζ + ( s , a ) and ζ − ( s , a ) are zero. We find that these lines may be grouped into four families, with the start and end points for each family being simply characterized. At values of a =1/2, 2/3 and 3/4, the curves pass through points which may also be characterized, in terms of zeros of the Riemann zeta function, or the Dirichlet functions L −3 (

APA, Harvard, Vancouver, ISO, and other styles

21

Moser, Jan. "On the distribution of multiplicities of zeros of Riemann zeta function." Czechoslovak Mathematical Journal 44, no. 3 (1994): 385–404. http://dx.doi.org/10.21136/cmj.1994.128478.

Full text

APA, Harvard, Vancouver, ISO, and other styles

22

SRICHAN, TEERAPAT. "ON THE ABSENCE OF ZEROS IN INFINITE ARITHMETIC PROGRESSION FOR CERTAIN ZETA FUNCTIONS." Bulletin of the Australian Mathematical Society 98, no. 3 (2018): 376–82. http://dx.doi.org/10.1017/s0004972718000643.

Full text

Abstract:

Putnam [‘On the non-periodicity of the zeros of the Riemann zeta-function’, Amer. J. Math.76 (1954), 97–99] proved that the sequence of consecutive positive zeros of $\unicode[STIX]{x1D701}(\frac{1}{2}+it)$ does not contain any infinite arithmetic progression. We extend this result to a certain class of zeta functions.

APA, Harvard, Vancouver, ISO, and other styles

23

Filevych, P. V. "Asymptotic estimates for entire functions of minimal growth with given zeros." Matematychni Studii 62, no. 1 (2024): 54–59. http://dx.doi.org/10.30970/ms.62.1.54-59.

Full text

Abstract:

Let $\zeta=(\zeta_n)$ be an arbitrary complex sequence such that $0<|\zeta_1|\le|\zeta_2|\le\dots$ and $\zeta_n\to\infty$ as $n\to\infty$, let $n_\zeta(r)$ and $N_\zeta(r)$ be the counting function and the integrated counting function of this sequence, respectively. By $\mathcal{E}_\zeta$ we denote the class of all entire functions whose zeros are precisely the $\zeta_n$, where a complex number that occurs $m$ times in the sequence $\zeta$ corresponds to a zero of multiplicity $m$. Suppose that $\Phi$ is a convex function on $\mathbb{R}$ such that $\Phi(\sigma)/\sigma\to+\infty$ as $\sigma\

APA, Harvard, Vancouver, ISO, and other styles

24

Šiaučiūnas, Darius, Raivydas Šimėnas, and Monika Tekorė. "Approximation of Analytic Functions by Shifts of Certain Compositions." Mathematics 9, no. 20 (2021): 2583. http://dx.doi.org/10.3390/math9202583.

Full text

Abstract:

In the paper, we obtain universality theorems for compositions of some classes of operators in multidimensional space of analytic functions with a collection of periodic zeta-functions. The used shifts of periodic zeta-functions involve the sequence of imaginary parts of non-trivial zeros of the Riemann zeta-function.

APA, Harvard, Vancouver, ISO, and other styles

25

Cheer, A. Y., and D. A. Goldston. "Simple zeros of the Riemann zeta-function." Proceedings of the American Mathematical Society 118, no. 2 (1993): 365. http://dx.doi.org/10.1090/s0002-9939-1993-1132849-0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Conrey, JB, A. Ghosh, and SM Gonek. "Simple Zeros of the Riemann Zeta-Function." Proceedings of the London Mathematical Society 76, no. 3 (1998): 497–522. http://dx.doi.org/10.1112/s0024611598000306.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Matsusaka, Toshiki. "Real zeros of the Hurwitz zeta function." Acta Arithmetica 183, no. 1 (2018): 53–62. http://dx.doi.org/10.4064/aa8647-11-2017.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Karatsuba, A. A. "The Riemann zeta function and its zeros." Russian Mathematical Surveys 40, no. 5 (1985): 23–82. http://dx.doi.org/10.1070/rm1985v040n05abeh003682.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Diaz-Vargas, Javier. "On zeros of characteristic p zeta function." Journal of Number Theory 117, no. 2 (2006): 241–62. http://dx.doi.org/10.1016/j.jnt.2005.06.008.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Wu, X. "DISTINCT ZEROS OF THE RIEMANN ZETA-FUNCTION." Quarterly Journal of Mathematics 66, no. 2 (2015): 759–71. http://dx.doi.org/10.1093/qmath/hav014.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Ford, Kevin, and Alexandru Zaharescu. "Unnormalized differences between zeros of L-functions." Compositio Mathematica 151, no. 2 (2014): 230–52. http://dx.doi.org/10.1112/s0010437x14007659.

Full text

Abstract:

AbstractWe study a subtle inequity in the distribution of unnormalized differences between imaginary parts of zeros of the Riemann zeta function, which was observed by a number of authors. We establish a precise measure which explains the phenomenon, that the location of each Riemann zero is encoded in the distribution of large Riemann zeros. We also extend these results to zeros of more general $L$-functions. In particular, we show how the rank of an elliptic curve over $\mathbb{Q}$ is encoded in the sequences of zeros of other$L$-functions, not only the one associated to the curve.

APA, Harvard, Vancouver, ISO, and other styles

32

Kuzovatov, Vyacheslav I., Alexander M. Kytmanov, and Azimbai Sadullaev. "On the Zeta-Function of Zeros of Entire Function." Journal of Siberian Federal University. Mathematics & Physics 14, no. 5 (2021): 599–603. http://dx.doi.org/10.17516/1997-1397-2021-14-5-599-603.

Full text

Abstract:

This article is devoted to the study of the properties of the zeta-function of zeros of entire function. We obtained an explicit expression for the kernel of the integral representation of the zetafunction in one case

APA, Harvard, Vancouver, ISO, and other styles

33

Thalassinakis, Emmanuel. "An In-Depth Investigation of the Riemann Zeta Function Using Infinite Numbers." Mathematics 13, no. 9 (2025): 1483. https://doi.org/10.3390/math13091483.

Full text

Abstract:

This study focuses on an in-depth investigation of the Riemann zeta function. For this purpose, infinite numbers and rotational infinite numbers, which have been introduced in previous studies published by the author, are used. These numbers are a powerful tool for solving problems involving infinity that are otherwise difficult to solve. Infinite numbers are a superset of complex numbers and can be either complex numbers or some quantification of infinity. The Riemann zeta function can be written as a sum of three rotational infinite numbers, each of which represents infinity. Using these inf

APA, Harvard, Vancouver, ISO, and other styles

34

Steuding, Jörn, and Janyarak Tongsomporn. "On the Order of Growth of Lerch Zeta Functions." Mathematics 11, no. 3 (2023): 723. http://dx.doi.org/10.3390/math11030723.

Full text

Abstract:

We extend Bourgain’s bound for the order of growth of the Riemann zeta function on the critical line to Lerch zeta functions. More precisely, we prove L(λ, α, 1/2 + it) ≪ t13/84+ϵ as t → ∞. For both, the Riemann zeta function as well as for the more general Lerch zeta function, it is conjectured that the right-hand side can be replaced by tϵ (which is the so-called Lindelöf hypothesis). The growth of an analytic function is closely related to the distribution of its zeros.

APA, Harvard, Vancouver, ISO, and other styles

35

KELLIHER, JAMES P., and RIAD MASRI. "Analytic continuation of multiple Hurwitz zeta functions." Mathematical Proceedings of the Cambridge Philosophical Society 145, no. 3 (2008): 605–17. http://dx.doi.org/10.1017/s0305004107001028.

Full text

Abstract:

AbstractWe use a variant of a method of Goncharov, Kontsevich and Zhao [5, 16] to meromorphically continue the multiple Hurwitz zeta function to $\mathbb{C}^{d}$, to locate the hyperplanes containing its possible poles and to compute the residues at the poles. We explain how to use the residues to locate trivial zeros of $\zeta_{d}(s;\theta)$.

APA, Harvard, Vancouver, ISO, and other styles

36

Macaitienė, Renata, and Darius Šiaučiūnas. "Joint universality of Hurwitz zeta-functions and nontrivial zeros of the Riemann zeta-function." Lithuanian Mathematical Journal 59, no. 1 (2019): 81–95. http://dx.doi.org/10.1007/s10986-019-09423-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

37

Laurinčikas, Antanas. "Zeros of the Riemann zeta-function in the discrete universality of the Hurwitz zeta-function." Studia Scientiarum Mathematicarum Hungarica 57, no. 2 (2020): 147–64. http://dx.doi.org/10.1556/012.2020.57.2.1460.

Full text

Abstract:

AbstractLet 0 < γ1 < γ2 < ··· ⩽ ··· be the imaginary parts of non-trivial zeros of the Riemann zeta-function. In the paper, we consider the approximation of analytic functions by shifts of the Hurwitz zeta-function ζ(s + iγkh, α), h > 0, with parameter α such that the set {log(m + α): m ∈ } is linearly independent over the field of rational numbers. For this, a weak form of the Montgomery conjecture on the pair correlation of {γk} is applied.

APA, Harvard, Vancouver, ISO, and other styles

38

Kim, T., C. S. Ryoo, L. C. Jang, and S. H. Rim. "Exploring theq-Riemann zeta function andq-Bernoulli polynomials." Discrete Dynamics in Nature and Society 2005, no. 2 (2005): 171–81. http://dx.doi.org/10.1155/ddns.2005.171.

Full text

Abstract:

We study that theq-Bernoulli polynomials, which were constructed by Kim, are analytic continued toβs(z). A new formula for theq-Riemann zeta functionζq(s)due to Kim in terms of nested series ofζq(n)is derived. The new concept of dynamics of the zeros of analytic continued polynomials is introduced, and an interesting phenomenon of “scattering” of the zeros ofβs(z)is observed. Following the idea ofq-zeta function due to Kim, we are going to use “Mathematica” to explore a formula forζq(n).

APA, Harvard, Vancouver, ISO, and other styles

39

Byrnes, Alyssa, Lin Jiu, Victor H. Moll, and Christophe Vignat. "Recursion rules for the hypergeometric zeta function." International Journal of Number Theory 10, no. 07 (2014): 1761–82. http://dx.doi.org/10.1142/s1793042114500547.

Full text

Abstract:

The hypergeometric zeta function is defined in terms of the zeros of the Kummer function M(a, a+b; z). It is established that this function is an entire function of order 1. The classical factorization theorem of Hadamard gives an expression as an infinite product. This provides linear and quadratic recurrences for the hypergeometric zeta function. A family of associated polynomials is characterized as Appell polynomials and the underlying distribution is given explicitly in terms of the zeros of the associated hypergeometric function. These properties are also given a probabilistic interpreta

APA, Harvard, Vancouver, ISO, and other styles

40

Garunkštis, Ramūnas. "On zeros of the derivative of the Lerch zeta-function." Lietuvos matematikos rinkinys 42 (December 20, 2002): 47–49. http://dx.doi.org/10.15388/lmr.2002.32817.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

AREF'EVA, I. YA, and I. V. VOLOVICH. "QUANTIZATION OF THE RIEMANN ZETA-FUNCTION AND COSMOLOGY." International Journal of Geometric Methods in Modern Physics 04, no. 05 (2007): 881–95. http://dx.doi.org/10.1142/s021988780700234x.

Full text

Abstract:

Quantization of the Riemann zeta-function is proposed. We treat the Riemann zeta-function as a symbol of a pseudodifferential operator and study the corresponding classical and quantum field theories. This approach is motivated by the theory of p-adic strings and by recent works on stringy cosmological models. We show that the Lagrangian for the zeta-function field is equivalent to the sum of the Klein–Gordon Lagrangians with masses defined by the zeros of the Riemann zeta-function. Quantization of the mathematics of Fermat–Wiles and the Langlands program is indicated. The Beilinson conjecture

APA, Harvard, Vancouver, ISO, and other styles

42

KUROKAWA, NOBUSHIGE, and MASATO WAKAYAMA. "A NOTE ON SPECTRAL ZETA FUNCTIONS OF QUANTUM GROUPS." International Journal of Mathematics 15, no. 02 (2004): 125–33. http://dx.doi.org/10.1142/s0129167x04002181.

Full text

Abstract:

We study analytic properties of spectral zeta functions associated to actions of the quantum group SUq(2) such as Z(s, SUq(2)), the zeta function corresponding to the regular representation introduced in [15]. As an application, we show the special value ζ(3) of the Riemann zeta function ζ(s) is given in terms of the classical limit of Z(s, SUq(2)). We further discuss a spectral zeta function [Formula: see text] associated with the so-called model of the representations of [Formula: see text] and show a presence of its series of "trivial" zeros, which is noteworthy.

APA, Harvard, Vancouver, ISO, and other styles

43

LESTER, STEPHEN. "On the distribution of the zeros of the derivative of the Riemann zeta-function." Mathematical Proceedings of the Cambridge Philosophical Society 157, no. 3 (2014): 425–42. http://dx.doi.org/10.1017/s0305004114000413.

Full text

Abstract:

AbstractWe establish an asymptotic formula describing the horizontal distribution of the zeros of the derivative of the Riemann zeta-function. For ℜ(s) = σ satisfying (log T)−1/3+ε ⩽ (2σ − 1) ⩽ (log log T)−2, we show that the number of zeros of ζ′(s) with imaginary part between zero and T and real part larger than σ is asymptotic to T/(2π(σ−1/2)) as T → ∞. This agrees with a prediction from random matrix theory due to Mezzadri. Hence, for σ in this range the zeros of ζ′(s) are horizontally distributed like the zeros of the derivative of characteristic polynomials of random unitary matrices are

APA, Harvard, Vancouver, ISO, and other styles

44

soltan, Shaimaa said. "New Odd Numbers Identity and the None-trivial Zeros of Zeta Function." Journal of Mathematics Research 15, no. 2 (2023): 74. http://dx.doi.org/10.5539/jmr.v15n2p74.

Full text

Abstract:

This paper is going to introduce a new identity unit circle function for complex plane specific for odd numbers.  Second, we are going to show some properties of these new unit Identity function.  Third, use this new unit Identity function to study the distribution of odd roots for sin term in zeta function but using the new identity function not Euler Identity to explain Riemann conjunction about the critical strip line and the none-trivial zeros along Re(S) = 0.5.  Also, In an Introductory Analysis for the geometric functions Sin and Cos, we will visualize

APA, Harvard, Vancouver, ISO, and other styles

45

Tongsomporn, Janyarak, Saeree Wananiyakul, and Jörn Steuding. "The Values of the Periodic Zeta-Function at the Nontrivial Zeros of Riemann’s Zeta-Function." Symmetry 13, no. 12 (2021): 2410. http://dx.doi.org/10.3390/sym13122410.

Full text

Abstract:

In this paper, we prove an asymptotic formula for the sum of the values of the periodic zeta-function at the nontrivial zeros of the Riemann zeta-function (up to some height) which are symmetrical on the real line and the critical line. This is an extension of the previous results due to Garunkštis, Kalpokas, and, more recently, Sowa. Whereas Sowa’s approach was assuming the yet unproved Riemann hypothesis, our result holds unconditionally.

APA, Harvard, Vancouver, ISO, and other styles

46

soltan, Shaimaa said. "Cubic and Quadratic Equations and Zeta Function Zeros." Journal of Mathematics Research 14, no. 5 (2022): 8. http://dx.doi.org/10.5539/jmr.v14n5p8.

Full text

Abstract:

In this paper, we will study a partial sum modulus distribution for a specific natural number set using a dynamically sliding window. Then we will construct a cubic equation from this distribution and a formula to calculate this cubic equation zero. Then we will go through some applications of this Cubic equation using the basic algebraic concepts to explain the distribution of natural numbers.  First part in this paper, we will interduce a partial sums modulus distribution for natural numbers using a dynamic sliding window as a parameter to explore the natural numbers distribution

APA, Harvard, Vancouver, ISO, and other styles

47

ŠLeŽeviČien˙E, R., and J. Steuding. "On the Zeros of the Estermann Zeta-Function." Integral Transforms and Special Functions 13, no. 4 (2002): 363–71. http://dx.doi.org/10.1080/10652460213524.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

Bui, H. M., and D. R. Heath-Brown. "On simple zeros of the Riemann zeta-function." Bulletin of the London Mathematical Society 45, no. 5 (2013): 953–61. http://dx.doi.org/10.1112/blms/bdt026.

Full text

APA, Harvard, Vancouver, ISO, and other styles

49

Hall, R. R. "On the Zeros of the Riemann Zeta-Function." Journal of the London Mathematical Society 59, no. 1 (1999): 65–75. http://dx.doi.org/10.1112/s0024610798006942.

Full text

APA, Harvard, Vancouver, ISO, and other styles

50

Conrey, J. B., A. Ghosh, and S. M. Gonek. "Large gaps between zeros of the zeta‐function." Mathematika 33, no. 2 (1986): 212–38. http://dx.doi.org/10.1112/s0025579300011219.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!