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Ramanujan type congruences for modular forms of several variables |
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| Authors: | Toshiyuki Kikuta Shoyu Nagaoka |
| Institution: | 1. Department of Mathematics, Osaka Institute of Technology, 5-16-1 Omiya, Asahi-ku, Osaka, 535-8585, Japan 2. Department of Mathematics, School of Science and Engineering, Kinki University, 3-4-1 Kowakae, Higashi-Osaka, Osaka, 577-8502, Japan |
| 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. |
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