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Gotowe bibliografie tematyczne / Zeros of zeta function

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Gotowa bibliografia na temat „Zeros of zeta function”

Autor: Grafiati

Data publikacji: 3 czerwca 2025

Data aktualizacji: 31 lipca 2025

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Artykuły w czasopismach na temat "Zeros of zeta function"

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.

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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.

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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.

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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

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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.

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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.

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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.

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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.

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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

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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.

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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.

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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.

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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

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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.

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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.

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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.

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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

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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.

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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.

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Rozprawy doktorskie na temat "Zeros of zeta function"

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Steuding, Jörn. "On simple zeros of the Riemann zeta-function." [S.l. : s.n.], 1999. http://deposit.ddb.de/cgi-bin/dokserv?idn=95589820X.

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Diaz-Vargas, Javier Arturo 1952. "On zeros of characteristic p zeta functions." Diss., The University of Arizona, 1996. http://hdl.handle.net/10150/290585.

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The location and multiplicity of the zeros of zeta functions encode interesting arithmetic information. We study characteristic p zeta functions of Carlitz and Goss. We present a simpler proof of the fact that "non-trivial" zeros of a characteristic p zeta function satisfy Goss' analogue of the Riemann Hypothesis for F(q)[T]. We also prove simplicity of these zeros, and give partial results for F(q)[T] where q is not necessarily prime. Then we focus on "trivial" zeros, but for characteristic p zeta functions for general function fields over finite fields. Here, we prove a theorem on zeros at n

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Wu, Dongsheng. "Eigenvalues of Differential Operators and Nontrivial Zeros of L-functions." BYU ScholarsArchive, 2020. https://scholarsarchive.byu.edu/etd/8729.

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The Hilbert-P\'olya conjecture asserts that the non-trivial zeros of the Riemann zeta function $\zeta(s)$ correspond (in a certain canonical way) to the eigenvalues of some positive operator. R. Meyer constructed a differential operator $D_-$ acting on a function space $\H$ and showed that the eigenvalues of the adjoint of $D_-$ are exactly the nontrivial zeros of $\zeta(s)$ with multiplicity correspondence. We follow Meyer's construction with a slight modification. Specifically, we define two function spaces $\H_\cap$ and $\H_-$ on $(0,\infty)$ and characterize them via the Mellin transform.

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Gulas, Michael Allen. "Using Hilbert Space Theory and Quantum Mechanics to Examine the Zeros of The Riemann-Zeta Function." Bowling Green State University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1594035551136634.

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Šimėnas, Raivydas. "Riemann'o hipotezės Speiser'io ekvivalentas." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2012~D_20140704_171541-67476.

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A. Speiser'is parodė, kad Riemann'o hipotezė yra ekvivalenti tam, kad Riemann'o dzeta funkcijos išvestinė neturi netrivialių nulių į kairę nuo kritinės tiesės. Kiekybinis šio fakto rezultatas buvo pasiektas N. Levinsono ir H. Montgomerio. Šie rezultatai buvo apibendrinti daugeliui dzeta funkcijų, kurioms tikimasi, kad Riemann'o hipotezė galioja. Šiame darbe mes apibendriname Speiser'io ekvivalentą dzeta-funkcijoms. Mes tiriame sąryšį tarp netrivialių nulių išplėstinės Selbergo klasės funkcijoms ir jų išvestinėms šiame regione. Šiai klasei priklauso ir funkcijos, kurioms Riemann'o hipotezė nete

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Newland, Derek B. "Kernels in the Selberg trace formula on the k-regular tree and zeros of the Ihara zeta function /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2005. http://wwwlib.umi.com/cr/ucsd/fullcit?p3189204.

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Bredberg, Johan. "On large gaps between consecutive zeros, on the critical line, of some zeta-functions." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:3e744bbd-c947-405c-b519-4808c8c5a73e.

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In this thesis we extend a method of Hall $[30, 34]$ which he used to show the existence of large gaps between consecutive zeros, on the critical line, of the Riemann zeta-function $zeta(s)$. Our modification involves introducing an "amplifier" and enables us to show the existence of gaps between consecutive zeros, on the critical line at height $T,$ of $zeta(s)$ of length at least $2.766 x (2pi/log{T})$. To handle some integral-calculations, we use the article $[44]$ by Hughes and Young. Also, we show that Hall's strategy can be applied not only to $zeta(s),$ but also to Dirichlet $L$-functio

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Alvites, José Carlos Valencia. "Hipótese de Riemann e física." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-13042012-084309/.

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Neste trabalho, introduzimos a função zeta de Riemann \'ZETA\'(s), para s \'PERTENCE\' C \\ e apresentamos muito do que é conhecido como justificativa para a hipótese de Riemann. A importância de \'ZETA\' (s) para a teoria analítica dos números é enfatizada e fornecemos uma prova conhecida do Teorema dos Números Primos. No final, discutimos a importância de \'ZETA\'(s) para alguns modelos físicos de interesse e concluimos descrevendo como a hipótese de Riemann pode ser acessada estudando estes sistemas<br>In this work, we introduce the Riemann zeta function \'ZETA\'(s), s \'IT BELONGS\' C \\

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Alcántara, Bode Julio. "A conjecture about the non-trivial zeroes of the Riemann zeta function." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/97185.

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Some heuristic arguments are given in support of the following conjecture: If the Riemann Hypothesis (RH) does not hold then the number of zeroes of the Riemann zeta function with real part σ > ½ is infinite.

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Reyes, Ernesto Oscar. "The Riemann zeta function." CSUSB ScholarWorks, 2004. https://scholarworks.lib.csusb.edu/etd-project/2648.

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The Riemann Zeta Function has a deep connection with the distribution of primes. This expository thesis will explain the techniques used in proving the properties of the Rieman Zeta Function, its analytic continuation to the complex plane, and the functional equation that the the Riemann Zeta Function satisfies.

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Książki na temat "Zeros of zeta function"

1

Voros, André. Zeta Functions over Zeros of Zeta Functions. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-05203-3.

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1967-, Van Frankenhuysen Machiel, ed. Fractal geometry and number theory: Complex dimensions of fractal strings and zeros of zeta functions. Birkhäuser, 2000.

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Laurinčikas, Antanas, and Ramūnas Garunkštis. The Lerch Zeta-function. Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-6401-8.

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Ramūnas, Garunkštis, ed. The Lerch zeta-function. Kluwer Academic Publishers, 2002.

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Montgomery, Hugh, Ashkan Nikeghbali, and Michael Th Rassias, eds. Exploring the Riemann Zeta Function. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59969-4.

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Keating, Jonathan P. Resummation and the turning-points of zeta function. Hewlett Packard, 1996.

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Motohashi, Y. Spectral theory of the Riemann zeta-function. Cambridge University Press, 1997.

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Laurinčikas, Antanas. Limit theorems for the Riemann zeta-function. Kluwer Academic, 1996.

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Laurinčikas, Antanas. Limit Theorems for the Riemann Zeta-Function. Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-017-2091-5.

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R, Heath-Brown D., ed. The theory of the Riemann zeta-function. 2nd ed. Clarendon Press, 1986.

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Części książek na temat "Zeros of zeta function"

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Laurinčikas, Antanas, and Ramūnas Garunkštis. "Distribution of Zeros." In The Lerch Zeta-function. Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-6401-8_8.

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Iwaniec, H. "Detecting critical zeros." In Lectures on the Riemann Zeta Function. American Mathematical Society, 2014. http://dx.doi.org/10.1090/ulect/062/17.

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Iwaniec, H. "Zeros off the critical line." In Lectures on the Riemann Zeta Function. American Mathematical Society, 2014. http://dx.doi.org/10.1090/ulect/062/14.

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Iwaniec, H. "Zeros on the critical line." In Lectures on the Riemann Zeta Function. American Mathematical Society, 2014. http://dx.doi.org/10.1090/ulect/062/15.

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Karabulut, Yunus, and Cem Yalçın Yıldırım. "Some Analogues of Pair Correlation of Zeta Zeros." In Exploring the Riemann Zeta Function. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59969-4_7.

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Iwaniec, H. "The product formula over the zeros." In Lectures on the Riemann Zeta Function. American Mathematical Society, 2014. http://dx.doi.org/10.1090/ulect/062/08.

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Iwaniec, H. "Positive proportion of the critical zeros." In Lectures on the Riemann Zeta Function. American Mathematical Society, 2014. http://dx.doi.org/10.1090/ulect/062/23.

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Lapidus, Michel L., and Machiel van Frankenhuijsen. "Critical Zeros of Zeta Functions." In Springer Monographs in Mathematics. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-2176-4_11.

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Cobler, Tim, and Michel L. Lapidus. "Towards a Fractal Cohomology: Spectra of Polya–Hilbert Operators, Regularized Determinants and Riemann Zeros." In Exploring the Riemann Zeta Function. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59969-4_3.

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Voros, André. "Riemann Zeros and Factorizations of the Zeta Function." In Lecture Notes of the Unione Matematica Italiana. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-05203-3_4.

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Streszczenia konferencji na temat "Zeros of zeta function"

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Xu, Hao. "Sigmoid function model of Zeta converter considering sneak circuits." In Second International Conference on Power Electronics and Artificial Intelligence (PEAI 2025), edited by Qiang Yang, Parikshit N. Mahalle, and Xuehe Wang. SPIE, 2025. https://doi.org/10.1117/12.3066774.

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Calingasan, Recto Rex M., and Alexander Vincent B. Policarpio. "On the zeros of the OEIS A191257 zeta function." In PROCEEDINGS OF THE 13TH IMT-GT INTERNATIONAL CONFERENCE ON MATHEMATICS, STATISTICS AND THEIR APPLICATIONS (ICMSA2017). Author(s), 2017. http://dx.doi.org/10.1063/1.5012157.

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Collins, Nick. "Sonification of the Riemann Zeta Function." In ICAD 2019: The 25th International Conference on Auditory Display. Department of Computer and Information Sciences, Northumbria University, 2019. http://dx.doi.org/10.21785/icad2019.003.

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The Riemann zeta function is one of the great wonders of mathematics, with a deep and still not fully solved connection to the prime numbers. It is defined via an infinite sum analogous to Fourier additive synthesis, and can be calculated in various ways. It was Riemann who extended the consideration of the series to complex number arguments, and the famous Riemann hypothesis states that the non-trivial zeroes of the function all occur on the critical line 0:5 + ti, and what is more, hold a deep correspondence with the prime numbers. For the purposes of sonification, the rich set of mathematic

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Gopani, Paras Himmat, Navpreet Singh, Hemanta Kumar Sarma, Digambar S. Negi, and Padmaja S. Mattey. "A Zeta Potentiometric Study on Effects of Ionic Composition and Rock-Saturation on Surface-Charge Interactions in Low-Salinity Water Flooding for Carbonate Formation." In SPE Western Regional Meeting. SPE, 2021. http://dx.doi.org/10.2118/200804-ms.

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Abstract As carbonate reservoirs are mostly oil-wet, the potential for the success of a waterflooding is lower. Therefore, a primary focus during waterflooding such reservoirs is on the ionic composition and salinity of injected brine which are able to impact the alteration of the rock wettability favorably by altering the surface charge towards a higher negative value or close to zero. The objective of this study is to employ zeta potentiometric studies comprising streaming potential and streaming current techniques to quantify the surface interactions and charges between the carbonate rock a

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Costa, G. A. T. F. Da. "Zeta function of a graph revisited." In CMAC Sul – Congresso de Matemática Aplicada e Computacional. SBMAC, 2014. http://dx.doi.org/10.5540/03.2014.002.01.0050.

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Xavier, G. Britto Antony, T. Sathinathan, and D. Arun. "Fractional order Riemann zeta factorial function." In SECOND INTERNATIONAL CONFERENCE OF MATHEMATICS (SICME2019). Author(s), 2019. http://dx.doi.org/10.1063/1.5097535.

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Ozden, Hacer, Ismail Naci Cangul, Yilmaz Simsek, George Maroulis, and Theodore E. Simos. "Hurwitz Type Multiple Genocchi Zeta Function." In COMPUTATIONAL METHODS IN SCIENCE AND ENGINEERING: Advances in Computational Science: Lectures presented at the International Conference on Computational Methods in Sciences and Engineering 2008 (ICCMSE 2008). AIP, 2009. http://dx.doi.org/10.1063/1.3225435.

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Peng Ren, Richard C. Wilson, and Edwin R. Hancock. "Pattern vectors from the Ihara zeta function." In 2008 19th International Conference on Pattern Recognition (ICPR). IEEE, 2008. http://dx.doi.org/10.1109/icpr.2008.4761902.

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Mingshun, Yang. "On Integral Representations for the Zeta-Function." In 2009 Second International Conference on Intelligent Computation Technology and Automation. IEEE, 2009. http://dx.doi.org/10.1109/icicta.2009.853.

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DETOMI, ELOISA, and ANDREA LUCCHINI. "SOME GENERALIZATIONS OF THE PROBABILISTIC ZETA FUNCTION." In Proceedings of a Conference in Honor of Akbar Rhemtulla. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812708670_0007.

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