Ramanujan type congruences for modular forms of several variables

2012/03/31 by Toshiyuki Kikuta, Kikuta, Toshiyuki, Shoyu Nagaoka +1
Mathematics · #11F33 #11F46 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F33 #msc:11F46

paper · pdf · doi:10.48550/arxiv.1204.0087

12 pages

arxiv created 2012/03/31 · arxiv updated 2012/04/03

Abstract

We give congruences between the Eisenstein series and a cusp form in the cases of Siegel modular forms and Hermitian modular forms. We should emphasize that there is a relation between the existence of a prime dividing the k-1-th generalized Bernoulli number and the existence of non-trivial Hermitian cusp forms of weight k. We will conclude by giving numerical examples for each case.

Related

• Ramanujan type congruences for the Klingen-Eisenstein series
• Ramanujan congruences for Siegel modular forms
• Relations among Ramanujan-Type Congruences I
• Congruences for Level 1 cusp forms of half-integral weight
• Ramanujan's congruence primes