On the values of a class of Dirichlet series at rational arguments
Authors:
K. Chakraborty, S. Kanemitsu and H.L. Li
Journal:
Proc. Amer. Math. Soc. 138 (2010), 12231230
MSC (2010):
Primary 11M35; Secondary 33B15
Published electronically:
December 4, 2009
MathSciNet review:
2578516
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Abstract: In this paper we shall prove that the combination of the general distribution property and the functional equation for the LipschitzLerch transcendent capture the whole spectrum of deeper results on the relations between the values at rational arguments of functions of a class of zetafunctions. By Theorem 1 and its corollaries, we can cover all the previous results in a rather simple and lucid way. By considering the limiting cases, we can also deduce new striking identities for Milnor's gamma functions, among which is the Gauss second formula for the digamma function.
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Additional Information
K. Chakraborty
Affiliation:
HarishChandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211 019, India
Email:
kalyan@hri.res.in
S. Kanemitsu
Affiliation:
Graduate School of Advanced Technology, Kinki University, Iizuka, Fukuoka 8208555, Japan
Email:
kanemitu@fuk.kindai.ac.jp
H.L. Li
Affiliation:
Department of Mathematics, Weinan Teachers College, Weinan, Shaanxi, 714000, People’s Republic of China
Email:
lihailong@wntc.edu.cn
DOI:
http://dx.doi.org/10.1090/S0002993909101715
Keywords:
LipschitzLerch transcendent,
Hurwitz zeta function,
polylogarithm function,
Gauss' second formula,
Milnor's gamma function.
Received by editor(s):
December 28, 2008
Received by editor(s) in revised form:
August 18, 2009
Published electronically:
December 4, 2009
Dedicated:
Dedicated to Professor Eiichi Bannai on his sixtieth birthday, with great respect and friendship
Communicated by:
Ken Ono
Article copyright:
© Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
