Integral representations of q-analogues of the Hurwitz zeta function

Monatshefte fur Mathematik

Volumn 149, Issue 2, 2006, Pages 141-154

  Wakayama, Masato ^a   Yamasaki, Yoshinori ^a  

^a KYUSHU UNIVERSITY   (Japan)

Author keywords

Bernoulli polynomials; Hurwitz's zeta function; Mellin transforms; Poisson's summation formula; q analogue

Indexed keywords

EID: 33749028492     PISSN: 00269255     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00605-005-0369-1     Document Type: Article

References (14)

1. Andrews GE, Askey R, Roy R (1999) Special Functions. Encyclopedia of Mathematics and its Applications, vol 71. Cambridge: Univ Press
2. Appell P (1882) Sur une classe de fonctions analogues aux fonctions Eulériennes, Math Ann 19: 84-102
3. Bradley DM (2005) Multiple q-zeta values. J Algebra 283: 752-798
4. Kaneko M, Kurokawa N, Wakayama M (2003) A variation of Euler's approach to values of the Riemann zeta function. Kyushu J Math 57: 175-192
5. Kawagoe K, Wakayama M, Yamasaki Y (2006) q-Analogues of the Riemann zeta, the Dirichlet L-functions, and a crystal zeta function. Forum Math, to appear
6. Koblitz N (1982) On Carlitz's q-Bernoulli numbers. J Number Theory 14: 332-339
7. Kurokawa N, Wakayama M (2004) Absolute tensor products. Int Math Res Not 5: 249-260
8. Hashimoto Y, Wakayama M (2005) Hierarchy of the Selberg zeta functions. Lett Math Phys 73: 59-70
9. Riemann B (1859) Über die Anzahl der Primzahlen unter einer gegebenen Grösse. Monatsber Akad Berlin, pp 671-680
10. Satoh J (1989) q-Analogue of Riemann's ζ-function and q-Euler numbers. J Number Theory 31: 346-362
11. Tsumura H (1999) A note on q-analogues of Dirichlet series. Proc Japan Acad Ser A Math Sci 75: 23-25
12. Tsumura H (2001) On modification of the q-L-series and its applications. Nagoya Math J 164: 185-197
13. Whittaker ET, Watson GN (1927) A Course of Modern Analysis. 4th edn. Cambridge: Univ Press
14. Zhao J (2003) q-Multiple Zeta functions and q-multiple polylogarithms. Preprint, math QA/0304448