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Bulletin of the London Mathematical Society Advance Access originally published online on April 12, 2008
Bulletin of the London Mathematical Society 2008 40(2):289-297; doi:10.1112/blms/bdn014
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© 2008 London Mathematical Society

On certain analogues of Eisenstein series and their evaluation formulas of Hurwitz type

Hirofumi Tsumura

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

Received 21 June 2007. Revision received 4 December 2007.

In this paper, we consider certain analogues of Eisenstein series involving hyperbolic sine and cosine functions. Using a result of Hurwitz, we prove some evaluation formulas for these series at positive integers. We can regard these formulas as analogues of the famous formulas for certain series given by Cauchy, Ramanujan, Berndt, and so on, as well as those for the Eisenstein series given by Hurwitz.

2000 Mathematics Subject Classification 11M41, 11M99.


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