On analogues of the Euler constant and Lerch's limit formula
Authors:
Nobushige Kurokawa and Masato Wakayama
Journal:
Proc. Amer. Math. Soc. 132 (2004), 935943
MSC (2000):
Primary 11M35, 33D05
Published electronically:
November 13, 2003
MathSciNet review:
2045407
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Abstract: We introduce and study a analogue of the Euler constant via a suitably defined analogue of the Riemann zeta function. We show, in particular, that the value is irrational. We also present a analogue of the Hurwitz zeta function and establish an analogue of the limit formula of Lerch in 1894 for the gamma function. This limit formula can be regarded as a natural generalization of the formula of .
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N. Kurokawa and M. Wakayama, A comparison between the sum over Selberg's zeroes and Riemann's zeroes, J. Ramanujan Math. Soc. 18 (2003), 221236. (Errata will also appear.)
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 Y. Hashimoto, Y. Iijima, N. Kurokawa and M. Wakayama, Euler's constants for the Selberg and the Dedekind zeta functions, Bulletin of the Belgian Mathematical Society Simon Stevin (to appear).
 [J]
 F. H. Jackson, On definite integrals, Quart. J. Pure Appl. Math. 41 (1910), 193203.
 [KKW]
 M. Kaneko, N. Kurokawa and M. Wakayama, A variation of Euler's approach to values of the Riemann zeta function, Kyushu Math. J. 57 (2003), 175192.
 [KW]
 N. Kurokawa and M. Wakayama, A comparison between the sum over Selberg's zeroes and Riemann's zeroes, J. Ramanujan Math. Soc. 18 (2003), 221236. (Errata will also appear.)
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Additional Information
Nobushige Kurokawa
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, Meguro, Tokyo, 1520033 Japan
Email:
kurokawa@math.titech.ac.jp
Masato Wakayama
Affiliation:
Faculty of Mathematics, Kyushu University, Hakozaki, Fukuoka, 8128581 Japan
Email:
wakayama@math.kyushuu.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002993903070254
PII:
S 00029939(03)070254
Keywords:
Euler's constant,
Riemann's zeta function,
Hurwitz's zeta function,
$q$gamma function,
Lerch's limit formula
Received by editor(s):
September 3, 2002
Published electronically:
November 13, 2003
Additional Notes:
Work in part supported by GrantinAid for Scientific Research (B) No. 11440010, and by GrantinAid for Exploratory Research No. 13874004, Japan Society for the Promotion of Science
Communicated by:
WenChing Winnie Li
Article copyright:
© Copyright 2003
American Mathematical Society
