Analogues of level-N Eisenstein series

Hirofumi Tsumura

Vol. 255 (2012), No. 2, 489–510

DOI: 10.2140/pjm.2012.255.489

Abstract

We consider certain analogues of level-N Eisenstein series involving hyperbolic functions. By developing the method used in our previous work, we prove some relation formulas for these series at positive integers which include our previous results corresponding to the cases of level 1 and 2. Furthermore, using these results, we evaluate certain two-variable analogues of level-N Eisenstein series.

Keywords

Eisenstein series, Riemann zeta function, hyperbolic functions

Mathematical Subject Classification 2010

Primary: 11M41

Secondary: 11M99

Milestones

Received: 18 March 2011

Revised: 2 December 2011

Accepted: 5 December 2011

Published: 10 April 2012