Skip Navigation



The Quarterly Journal of Mathematics Advance Access published online on December 11, 2007
The Quarterly Journal of Mathematics, doi:10.1093/qmath/ham025
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
59/1/55    most recent
ham025v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Matsumoto, K.
Right arrow Articles by Tsumura, H.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2007. Published by Oxford University Press. All rights reserved For permissions, please email: journals.permissions@oxfordjournals.org

A NEW METHOD OF PRODUCING FUNCTIONAL RELATIONS AMONG MULTIPLE ZETA-FUNCTIONS

Kohji Matsumoto {dagger}

Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan

Hirofumi Tsumura{ddagger}

Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1, Minami-Ohsawa, Hachioji, Tokyo 192-0397, Japan

{ddagger} Corresponding author. E-mail: tsumura{at}tmu.ac.jp

Received 2 March 2007; revised 23 April 2007
  Abstract

In this paper, we introduce a new method of producing functional relations among multiple zeta-functions. This method can be regarded as a kind of multiple analogue of Hardy's one of proving the functional equation for the Riemann zeta-function. Using this method, we give new functional relations for multiple zeta-functions. In particular, substituting positive integers into variables of them, we obtain known relation formulas for the multiple zeta-values. Furthermore, applying our method to a certain series involving hyperbolic sine functions, we can obtain certain multiple analogues of the known results given by Cauchy, Ramanujan, Berndt and so on.

{dagger} E-mail: kohjimat{at}math.nagoya-u.ac.jp


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.