On the values of a class of Dirichlet series at rational arguments-Reference-Cited by-同舟云学术

On the values of a class of Dirichlet series at rational arguments

Published:2009-12-04 Issue:4 Volume:138 Page:1223-1230
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Chakraborty K.,Kanemitsu S.,Li H.-L.

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2010-138-04/S0002-9939-09-10171-5/S0002-9939-09-10171-5.pdf

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