Relations among Ramanujan-type Congruences
Martin Raum (Chalmers Technical University, Gothenburg, Sweden)
Abstract: We present a new framework to access relations among Ramanujan-type congruences of a weakly holomorphic modular form. The framework is strong enough to apply to all Shimura varieties, and covers half-integral weights if unary theta series are available. We demonstrate effectiveness in the case of elliptic modular forms of integral weight, where we obtain a characterization of Ramanujan-type congruences in terms of Hecke congruences. Finally, we showcase concrete computer calculations, exploring the information encoded by our framework in the case of elliptic modular forms of half-integral weight. This leads to an unexpected dichotomy between Ramanujan-type congruences found by Atkin and by Ono, Ahlgren-Ono.
number theory
Audience: researchers in the topic
Series comments: Password: the number of quadratic nonresidues modulo 23
| Organizer: | Fedor Petrov* |
| *contact for this listing |