On the values of a class of Dirichlet series at rational arguments
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- by K. Chakraborty, S. Kanemitsu and H.-L. Li PDF
- Proc. Amer. Math. Soc. 138 (2010), 1223-1230 Request permission
Abstract:
In this paper we shall prove that the combination of the general distribution property and the functional equation for the Lipschitz-Lerch transcendent capture the whole spectrum of deeper results on the relations between the values at rational arguments of functions of a class of zeta-functions. 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.References
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Additional Information
- K. Chakraborty
- Affiliation: Harish-Chandra 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 820-8555, 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
- Received by editor(s): December 28, 2008
- Received by editor(s) in revised form: August 18, 2009
- Published electronically: December 4, 2009
- Communicated by: Ken Ono
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1223-1230
- MSC (2010): Primary 11M35; Secondary 33B15
- DOI: https://doi.org/10.1090/S0002-9939-09-10171-5
- MathSciNet review: 2578516
Dedicated: Dedicated to Professor Eiichi Bannai on his sixtieth birthday, with great respect and friendship