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Journal articles on the topic 'Rieman's Zeta Function'

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Published: 4 June 2021

Last updated: 13 February 2022

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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 (April 8, 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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2

RODGERS, BRAD. "A CENTRAL LIMIT THEOREM FOR THE ZEROES OF THE ZETA FUNCTION." International Journal of Number Theory 10, no. 02 (February 20, 2014): 483–511. http://dx.doi.org/10.1142/s1793042113501054.

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On the assumption of the Riemann hypothesis, we generalize a central limit theorem of Fujii regarding the number of zeroes of Riemann's zeta function that lie in a mesoscopic interval. The result mirrors results of Spohn and Soshnikov and others in random matrix theory. In an appendix we put forward some general theorems regarding our knowledge of the zeta zeroes in the mesoscopic regime.

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3

TSUMURA, HIROFUMI. "On functional relations between the Mordell–Tornheim double zeta functions and the Riemann zeta function." Mathematical Proceedings of the Cambridge Philosophical Society 142, no. 3 (May 2007): 395–405. http://dx.doi.org/10.1017/s0305004107000059.

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AbstractIn this paper, we give certain analytic functional relations between the Mordell–Tornheim double zeta functions and the Riemann zeta function. These can be regarded as continuous generalizations of the known discrete relations between the Mordell–Tornheim double zeta values and the Riemann zeta values at positive integers discovered in the 1950's.

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4

Bump, Daniel, and Eugene K. S. Ng. "On Riemann's zeta function." Mathematische Zeitschrift 192, no. 2 (June 1986): 195–204. http://dx.doi.org/10.1007/bf01179422.

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5

Laurinčikas, Antanas, and Renata Macaitienė˙. "Joint universality of the Riemann zeta-function and Lerch zeta-functions." Nonlinear Analysis: Modelling and Control 18, no. 3 (July 25, 2013): 314–26. http://dx.doi.org/10.15388/na.18.3.14012.

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In the paper, we prove a joint universality theorem for the Riemann zeta-function and a collection of Lerch zeta-functions with parameters algebraically independent over the field of rational numbers.

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6

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.

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7

Acedo, Luis. "On an Exact Relation between ζ″(2) and the Meijer G -Functions." Mathematics 7, no. 4 (April 24, 2019): 371. http://dx.doi.org/10.3390/math7040371.

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In this paper we consider some integral representations for the evaluation of the coefficients of the Taylor series for the Riemann zeta function about a point in the complex half-plane ℜ ( s ) > 1 . Using the standard approach based upon the Euler-MacLaurin summation, we can write these coefficients as Γ ( n + 1 ) plus a relatively smaller contribution, ξ n . The dominant part yields the well-known Riemann’s zeta pole at s = 1 . We discuss some recurrence relations that can be proved from this standard approach in order to evaluate ζ ″ ( 2 ) in terms of the Euler and Glaisher-Kinkelin constants and the Meijer G -functions.

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8

Gelbart, Stephen S., and Stephen D. Miller. "Riemann's zeta function and beyond." Bulletin of the American Mathematical Society 41, no. 01 (October 30, 2003): 59–113. http://dx.doi.org/10.1090/s0273-0979-03-00995-9.

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9

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 (August 2007): 881–95. http://dx.doi.org/10.1142/s021988780700234x.

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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 conjectures on the values of L-functions of motives are interpreted as dealing with the cosmological constant problem. Possible cosmological applications of the zeta-function field theory are discussed.

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10

Noda, Takumi. "Some generating functions of the Riemann zeta function." Banach Center Publications 118 (2019): 107–11. http://dx.doi.org/10.4064/bc118-6.

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11

Ye, Zhuan. "The Nevanlinna Functions of the Riemann Zeta-Function." Journal of Mathematical Analysis and Applications 233, no. 1 (May 1999): 425–35. http://dx.doi.org/10.1006/jmaa.1999.6343.

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12

Kim, Taekyun. "q-Riemann zeta function." International Journal of Mathematics and Mathematical Sciences 2004, no. 12 (2004): 599–605. http://dx.doi.org/10.1155/s0161171204307180.

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We consider the modifiedq-analogue of Riemann zeta function which is defined byζq(s)=∑n=1∞(qn(s−1)/[n]s),0<q<1,s∈ℂ. In this paper, we giveq-Bernoulli numbers which can be viewed as interpolation of the aboveq-analogue of Riemann zeta function at negative integers in the same way that Riemann zeta function interpolates Bernoulli numbers at negative integers. Also, we will treat some identities ofq-Bernoulli numbers using nonarchimedeanq-integration.

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13

PERELMAN, CARLOS CASTRO. "THE RIEMANN HYPOTHESIS IS A CONSEQUENCE OF $\mathcal{CT}$-INVARIANT QUANTUM MECHANICS." International Journal of Geometric Methods in Modern Physics 05, no. 01 (February 2008): 17–32. http://dx.doi.org/10.1142/s021988780800262x.

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The Riemann's hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form sn = 1/2 + iλn. By constructing a continuous family of scaling-like operators involving the Gauss–Jacobi theta series and by invoking a novel [Formula: see text]-invariant Quantum Mechanics, involving a judicious charge conjugation [Formula: see text] and time reversal [Formula: see text] operation, we show why the Riemann Hypothesis is true. An infinite family of theta series and their Mellin transform leads to the same conclusions.

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14

Genys, Jonas, Renata Macaitienė, Santa Račkauskienė, and Darius Šiaučiūnas. "A MIXED JOINT UNIVERSALITY THEOREM FOR ZETA‐FUNCTIONS." Mathematical Modelling and Analysis 15, no. 4 (November 15, 2010): 431–46. http://dx.doi.org/10.3846/1392-6292.2010.15.431-446.

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15

Patterson, S. J. "THE RIEMANN ZETA FUNCTION." Bulletin of the London Mathematical Society 26, no. 2 (March 1994): 196–97. http://dx.doi.org/10.1112/blms/26.2.196.

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16

Xavier, G. Britto Antony, T. Sathinathan, and D. Arun. "Riemann zeta factorial function." Journal of Physics: Conference Series 1139 (December 2018): 012047. http://dx.doi.org/10.1088/1742-6596/1139/1/012047.

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17

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 (October 20, 2013): 1350128. http://dx.doi.org/10.1142/s0217751x13501285.

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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 sequence of the nontrivial zeros of the Riemann zeta function can be interpreted as the spectrum of a self-adjoint operator of some hypothetical system described by the functional approach to quantum field theory. However, if one considers the same situation with numerical sequences whose asymptotic distributions are not "far away" from the asymptotic distribution of prime numbers, the associated functional integral cannot be constructed. Finally, we discuss possible relations between the asymptotic behavior of a sequence and the analytic domain of the associated zeta function.

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18

Laurinčikas, Antanas. "On joint universality of the Riemann zeta-function and Hurwitz zeta-functions." Journal of Number Theory 132, no. 12 (December 2012): 2842–53. http://dx.doi.org/10.1016/j.jnt.2012.05.026.

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19

HASSEN, ABDUL, and HIEU D. NGUYEN. "A ZERO-FREE REGION FOR HYPERGEOMETRIC ZETA FUNCTIONS." International Journal of Number Theory 07, no. 04 (June 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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20

Sofo, Anthony. "Shifted quadratic Zeta series." International Journal of Mathematics and Mathematical Sciences 2004, no. 67 (2004): 3631–52. http://dx.doi.org/10.1155/s0161171204402026.

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It is well known that the Riemann Zeta functionς(p)=∑n=1∞1/npcan be represented in closed form forpan even integer. We will define a shifted quadratic Zeta series as∑n=1∞1/(4n2−α2)p. In this paper, we will determine closed-form representations of shifted quadratic Zeta series from a recursion point of view using the Riemann Zeta function. We will also determine closed-form representations of alternating sign shifted quadratic Zeta series.

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21

HASSEN, ABDUL, and HIEU D. NGUYEN. "HYPERGEOMETRIC ZETA FUNCTIONS." International Journal of Number Theory 06, no. 01 (February 2010): 99–126. http://dx.doi.org/10.1142/s179304211000282x.

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This paper investigates a new family of special functions referred to as hypergeometric zeta functions. Derived from the integral representation of the classical Riemann zeta function, hypergeometric zeta functions exhibit many properties analogous to their classical counterpart, including the intimate connection to Bernoulli numbers. These new properties are treated in detail and are used to demonstrate a functional inequality satisfied by second-order hypergeometric zeta functions.

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22

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 (September 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 forms.

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23

Coffey, M. W., and M. C. Lettington. "Binomial polynomials mimicking Riemann's zeta function." Integral Transforms and Special Functions 31, no. 11 (April 23, 2020): 856–72. http://dx.doi.org/10.1080/10652469.2020.1755672.

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24

Jutila, M. "THE RIEMANN ZETA-FUNCTION The Theory of the Riemann Zeta-Function with Applications." Bulletin of the London Mathematical Society 18, no. 2 (March 1986): 219–20. http://dx.doi.org/10.1112/blms/18.2.219.

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25

Kurokawa, S. "From Pythagorean theorem to Riemann's conjecture-Riemann zeta function as a biological system." Seibutsu Butsuri 41, supplement (2001): S16. http://dx.doi.org/10.2142/biophys.41.s16_3.

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26

Chaudhry, M. Aslam, Asghar Qadir, M. T. Boudjelkha, M. Rafique, and S. M. Zubair. "Extended Riemann Zeta Functions." Rocky Mountain Journal of Mathematics 31, no. 4 (December 2001): 1237–63. http://dx.doi.org/10.1216/rmjm/1021249439.

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27

Mishou, H. "The joint value-distribution of the Riemann zeta function and Hurwitz zeta functions." Lithuanian Mathematical Journal 47, no. 1 (January 2007): 32–47. http://dx.doi.org/10.1007/s10986-007-0003-0.

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28

NAKAMURA, TAKASHI, and ŁUKASZ PAŃKOWSKI. "SELF-APPROXIMATION FOR THE RIEMANN ZETA FUNCTION." Bulletin of the Australian Mathematical Society 87, no. 3 (October 31, 2012): 452–61. http://dx.doi.org/10.1017/s0004972712000846.

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AbstractIn the paper we deal with self-approximation of the Riemann zeta function in the half plane $\operatorname {Re} s\gt 1$ and in the right half of the critical strip. We also prove some results concerning joint universality and joint value approximation of functions $\zeta (s+\lambda +id\tau )$ and $\zeta (s+i\tau )$.

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29

Vassilev-Missana, Mladen. "A note on prime zeta function and Riemann zeta function. Corrigendum." Notes on Number Theory and Discrete Mathematics 27, no. 2 (June 2021): 51–53. http://dx.doi.org/10.7546/nntdm.2021.27.2.51-53.

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30

Frontczak, R., and T. Goy. "General infinite series evaluations involving Fibonacci numbers and the Riemann zeta function." Matematychni Studii 55, no. 2 (June 22, 2021): 115–23. http://dx.doi.org/10.30970/ms.55.2.115-123.

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The purpose of this paper is to present closed forms for various types of infinite seriesinvolving Fibonacci (Lucas) numbers and the Riemann zeta function at integer arguments.To prove our results, we will apply some conventional arguments and combine the Binet formulasfor these sequences with generating functions involving the Riemann zeta function and some known series evaluations.Among the results derived in this paper, we will establish that $\displaystyle\sum_{k=1}^\infty (\zeta(2k+1)-1) F_{2k} = \frac{1}{2},\quad\sum_{k=1}^\infty (\zeta(2k+1)-1) \frac{L_{2k+1}}{2k+1} = 1-\gamma,$ where $\gamma$ is the familiar Euler-Mascheroni constant.

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31

Basiuk, Yu V., and S. I. Tarasyuk. "Fourier coefficients associated with the Riemann zeta-function." Carpathian Mathematical Publications 8, no. 1 (June 30, 2016): 16–20. http://dx.doi.org/10.15330/cmp.8.1.16-20.

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We study the Riemann zeta-function $\zeta(s)$ by a Fourier series method. The summation of $\log|\zeta(s)|$ with the kernel $1/|s|^{6}$ on the critical line $\mathrm{Re}\; s = \frac{1}{2}$ is the main result of our investigation. Also we obtain a new restatement of the Riemann Hypothesis.

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32

Panzone, Pablo A. "Fourier transforms related to ζ(s)." Proceedings of the Edinburgh Mathematical Society 64, no. 2 (April 30, 2021): 200–216. http://dx.doi.org/10.1017/s0013091521000092.

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AbstractUsing some formulas of S. Ramanujan, we compute in closed form the Fourier transform of functions related to Riemann zeta function $\zeta (s)=\sum \nolimits _{n=1}^{\infty } {1}/{n^{s}}$ and other Dirichlet series.

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33

ROCHON, Dominic. "A Bicomplex Riemann Zeta Function." Tokyo Journal of Mathematics 27, no. 2 (December 2004): 357–69. http://dx.doi.org/10.3836/tjm/1244208394.

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34

Akatsuka, Hirotaka. "The double Riemann zeta function." Communications in Number Theory and Physics 3, no. 4 (2009): 619–53. http://dx.doi.org/10.4310/cntp.2009.v3.n4.a2.

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35

Reid, Frederick Lyall, and Robert A. Van Gorder. "A Multicomplex Riemann Zeta Function." Advances in Applied Clifford Algebras 23, no. 1 (October 16, 2012): 237–51. http://dx.doi.org/10.1007/s00006-012-0369-x.

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36

Srivastava, Rekha, Humera Naaz, Sabeena Kazi, and Asifa Tassaddiq. "Some New Results Involving the Generalized Bose–Einstein and Fermi–Dirac Functions." Axioms 8, no. 2 (May 21, 2019): 63. http://dx.doi.org/10.3390/axioms8020063.

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In this paper, we obtain a new series representation for the generalized Bose–Einstein and Fermi–Dirac functions by using fractional Weyl transform. To achieve this purpose, we obtain an analytic continuation for these functions by generalizing the domain of Riemann zeta functions from ( 0 < ℜ ( s ) < 1 ) to ( 0 < ℜ ( s ) < μ ) . This leads to fresh insights for a new generalization of the Riemann zeta function. The results are validated by obtaining the classical series representation of the polylogarithm and Hurwitz–Lerch zeta functions as special cases. Fractional derivatives and the relationship of the generalized Bose–Einstein and Fermi–Dirac functions with Apostol–Euler–Nörlund polynomials are established to prove new identities.

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37

Alkan, Emre. "Biased behavior of weighted Mertens sums." International Journal of Number Theory 16, no. 03 (September 25, 2019): 547–77. http://dx.doi.org/10.1142/s1793042120500281.

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Using convexity properties of reciprocals of zeta functions, especially the reciprocal of the Riemann zeta function, we show that certain weighted Mertens sums are biased in favor of square-free integers with an odd number of prime factors. We study such type of bias for different ranges of the parameters and then consider generalizations to Mertens sums supported on semigroups of integers generated by relatively large subsets of prime numbers. We further obtain a wider range for the parameters both unconditionally and then conditionally on the Riemann Hypothesis. At the same time, we extend to certain semigroups, two classical summation formulas originating from the works of Landau concerning the behavior of derivatives of the reciprocal of the Riemann zeta function at [Formula: see text].

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38

Ibrahim, Rabha, and Maslina Darus. "On operator defined by double Zeta functions." Tamkang Journal of Mathematics 42, no. 2 (August 25, 2010): 163–74. http://dx.doi.org/10.5556/j.tkjm.42.2011.645.

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The aim of this paper is introducing an operator defined by generalized double zeta function involving the Riemann, Hurwitz, Hurwitz-Lerch and Barnes double zeta functions for analytic functions in the unit disc. Certain new subclasses of A using this operator are suggested. Some interesting properties of these classes are studied.

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39

Garunkštis, Ramūnas, and Antanas Laurinčikas. "The Riemann hypothesis and universality of the Riemann zeta-function." Mathematica Slovaca 68, no. 4 (August 28, 2018): 741–48. http://dx.doi.org/10.1515/ms-2017-0141.

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Abstract We prove that, under the Riemann hypothesis, a wide class of analytic functions can be approximated by shifts ζ(s + iγk), k ∈ ℕ, of the Riemann zeta-function, where γk are imaginary parts of nontrivial zeros of ζ(s).

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40

Guedes, Edigles, Raja Rama Gandhi, and Srinivas Kishan Anapu. "Investigations on the Theory of Riemann Zeta Function I: New Functional Equation, Integral Representation and Laurent Expansion for Riemann’s Zeta Function." Bulletin of Mathematical Sciences and Applications 5 (August 2013): 17–21. http://dx.doi.org/10.18052/www.scipress.com/bmsa.5.17.

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41

Maulidi, Ikhsan, Vina Apriliani, and Muhamad Syazali. "Fungsi Zeta Riemann Genap Menggunakan Bilangan Bernoulli." Desimal: Jurnal Matematika 2, no. 1 (February 4, 2019): 43–47. http://dx.doi.org/10.24042/djm.v2i1.3589.

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In this article, we study about the value of Riemann Zeta Function for even numbers using Bernoulli number. First, we give some basic theory about Bernoulli number and Riemann Zeta function. The method that used in this research was literature study. From our analysis, we have a theorem to evaluate the value of Riemann Zeta function for the even numbers with its proving.

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42

Friedli, Fabien, and Anders Karlsson. "Spectral zeta functions of graphs and the Riemann zeta function in the critical strip." Tohoku Mathematical Journal 69, no. 4 (December 2017): 585–610. http://dx.doi.org/10.2748/tmj/1512183631.

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43

Mishou, Hidehiko. "The joint value distribution of the Riemann zeta function and Hurwitz zeta functions II." Archiv der Mathematik 90, no. 3 (February 14, 2008): 230–38. http://dx.doi.org/10.1007/s00013-007-2397-7.

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44

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 (January 2019): 81–95. http://dx.doi.org/10.1007/s10986-019-09423-2.

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45

Cherednik, I. "On q-analogues of Riemann's zeta function." Selecta Mathematica 7, no. 4 (December 2001): 447–91. http://dx.doi.org/10.1007/s00029-001-8095-6.

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46

Bucur, Alina, Anne-Maria Ernvall-Hytönen, Almasa Odžak, and Lejla Smajlović. "On a Li-type criterion for zero-free regions of certain Dirichlet series with real coefficients." LMS Journal of Computation and Mathematics 19, no. 1 (2016): 259–80. http://dx.doi.org/10.1112/s1461157016000115.

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The Li coefficients $\unicode[STIX]{x1D706}_{F}(n)$ of a zeta or $L$-function $F$ provide an equivalent criterion for the (generalized) Riemann hypothesis. In this paper we define these coefficients, and their generalizations, the $\unicode[STIX]{x1D70F}$-Li coefficients, for a subclass of the extended Selberg class which is known to contain functions violating the Riemann hypothesis such as the Davenport–Heilbronn zeta function. The behavior of the $\unicode[STIX]{x1D70F}$-Li coefficients varies depending on whether the function in question has any zeros in the half-plane $\text{Re}(z)>\unicode[STIX]{x1D70F}/2.$ We investigate analytically and numerically the behavior of these coefficients for such functions in both the $n$ and $\unicode[STIX]{x1D70F}$ aspects.

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47

Milgram, Michael. "An Integral Equation for Riemann’s Zeta Function and Its Approximate Solution." Abstract and Applied Analysis 2020 (May 15, 2020): 1–29. http://dx.doi.org/10.1155/2020/1832982.

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Two identities extracted from the literature are coupled to obtain an integral equation for Riemann’s ξs function and thus ζs indirectly. The equation has a number of simple properties from which useful derivations flow, the most notable of which relates ζs anywhere in the critical strip to its values on a line anywhere else in the complex plane. From this, both an analytic expression for ζσ+it, everywhere inside the asymptotic t⟶∞ critical strip, as well as an approximate solution can be obtained, within the confines of which the Riemann Hypothesis is shown to be true. The approximate solution predicts a simple, but strong correlation between the real and imaginary components of ζσ+it for different values of σ and equal values of t; this is illustrated in a number of figures.

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48

de Reyna, J. Arias. "High precision computation of Riemann’s zeta function by the Riemann-Siegel formula, I." Mathematics of Computation 80, no. 274 (May 1, 2011): 995. http://dx.doi.org/10.1090/s0025-5718-2010-02426-3.

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49

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

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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.

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50

MERA, MITSUGU. "ZERO-FREE REGIONS OF A q-ANALOGUE OF THE COMPLETE RIEMANN ZETA FUNCTION." International Journal of Number Theory 07, no. 04 (June 2011): 1075–92. http://dx.doi.org/10.1142/s1793042111004344.

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A q-analogue of the complete Riemann zeta function presented in this paper is defined by the q-Mellin transform of the Jacobi theta function. We study zero-free regions of the q-zeta function. As a by-product, we show that the Riemann zeta function does not vanish in a sub-region of the critical strip.

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