References
- M.H. Annaby and Z.S. Mansour, On zeros of second and third Jackson q-Bessel, functions and their q-integral transforms, Math. Proc. Cambridge Philos. Soc. 147 (2009), 47–67. doi: https://doi.org/10.1017/S0305004109002357
- M.H. Annaby, Z.S. Mansour, and O.A. Ashour, Sampling theorems associated with biorthogonal q-Bessel functions, J. Phys. A 43(29) (2010), 295204. doi: https://doi.org/10.1088/1751-8113/43/29/295204
- T. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976.
- M. Cenkci and M. Can, Some results on q-analogue of the Lerch Zeta function, Adv. Stud. Contemp. Math. 12 (2006), 213–223.
- J.L. Cieśliński, Improved q-exponential and q-trigonometric functions, Appl. Math. Lett. 24(12) (2011), 2110–2114. doi: https://doi.org/10.1016/j.aml.2011.06.009
- G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge, 2004.
- Y. Gon, N. Kurokawa, and H. Oyanagi, Multiple q-Mahler measures and Zeta functions, J. Number Theory 124 (2007), 328–345. doi: https://doi.org/10.1016/j.jnt.2006.09.004
- M.E.H. Ismail, The zeros of basic Bessel functions, the functions Jν+α(x) and associated orthogonal polynomials, J. Math. Anal. Appl. 86 (1982), 11–19. doi: https://doi.org/10.1016/0022-247X(82)90248-7
- M.E.H. Ismail, Classical and Quantum Orthogonal Polynomials in One Variable, Cambridge University Press, Cambridge, 2005.
- M.E.H. Ismail and Z.S.I. Mansour, q-analogs of Lidstone expansion theorem, two point Taylor expansion theorem, and Bernoulli polynomials, Analysis and Applications 17(6) (2019), 853–895. doi: https://doi.org/10.1142/S0219530518500264
- F.H. Jackson, A basic-sine and cosine with symbolical solutions of certain differential equations, Proc. Edinb. Math. Soc. 22 (1903), 28–39. doi: https://doi.org/10.1017/S0013091500001930
- K. Kawagoe, M. Wakayama, and Y. Yamasaki, q-analogues of the Riemann zeta, the Dirichlet L-functions, and a crystal zeta function, Forum Math. 20(1) (2008), 1–26. doi: https://doi.org/10.1515/FORUM.2008.001
- M. Kaneko, N. Kurokawa, and M. Wakayama, A variation of Euler’s approach to values of the Riemann zeta function, Kyushu J. Math. 57(1) (2003), 175–192. doi: https://doi.org/10.2206/kyushujm.57.175
- N. Kishore, The Reyleigh function, Amer. Math. Soc. 145 (1963), 27–33.
- A. Kvitsinsky, Spectral zeta functions for q-Bessel equations, J. Phys. A 28(6) (1995), 1753–1764. doi: https://doi.org/10.1088/0305-4470/28/6/026
- A. Kvitsinsky, Zeta functions, heat kernel expansions, and asymptotics for q- Bessel functions, J. Math. Anal. Appl. 196(3) (1995), 947–964. doi: https://doi.org/10.1006/jmaa.1995.1453
- S. Nalci and O. Pashaev, q-Bernoulli numbers and zeros of q-sine function, arXiv:1202.2265 [math.QA], 2012.
- A.Yu. Pupyrev, On the linear and algebraic independence of q-zeta values, Mat. Zametki 78(4) (2005), 608–613; translation in Math. Notes 78(3–4) (2005), 563– 568. doi: https://doi.org/10.4213/mzm2619
- J. Satoh, q-analogue of Riemann’s ζ-function and q-Euler numbers, J. Number Theory 31 (1989), 346–362. doi: https://doi.org/10.1016/0022-314X(89)90078-4
- J. Sondow, Zeros of alternating zeta function on the line Res = 1, Amer. Math. Monthly 15(5) (2003), 435–437.
- H.M. Srivastava and J. Choi, Zeta and q-Zeta functions and associated series and integrals, Elsevier, Amsterdam, 2012.
- H.M. Srivastava, T. Kim, and Y. Simsek, q-Bernoulli numbers and polynomials associated with multiple q-Zeta functions and basic l-series, Russian J. Math. Phys. 12 (2005), 201–228.
- E.C. Titchmarsh, The theory of the Riemann zeta-function, second edition, The Clarendon Press, New York, 1986. Edited and with a preface by D.R. Heath-Brown.
- H. Tsumura, A note on q-analogues of the Dirichlet series and q-Bernoulli numbers, J. Number Theory 39 (1991), 251–256. doi: https://doi.org/10.1016/0022-314X(91)90048-G
- H. Tsumura, On evaluation of the Dirichlet series at positive integers by q- calculation, J. Number Theory 48 (1994), 383–391. doi: https://doi.org/10.1006/jnth.1994.1074
- H. Tsumura, A note on q-analogues of Dirichlet series, Proc. Japan Acad. Ser. A Math. Sci. 75 (1999), 23–25. doi: https://doi.org/10.3792/pjaa.75.23
- M. Wakayama and Y. Yamasaki, Integral representations of q-analogues of the Hurwitz zeta function, Monatsh. Math. 149(2) (2006), 141–154. doi: https://doi.org/10.1007/s00605-005-0369-1