Crynodeb
We prove that if a prime ℓ>3 divides pk-1, where p is prime, then there is a congruence modulo ℓ, like Ramanujan's mod 691 congruence, for the Hecke eigenvalues of some cusp form of weight k and level p. We relate ℓ to primes like 691 by viewing it as a divisor of a partial zeta value, and see how a construction of Ribet links the congruence with the Bloch-Kato conjecture (theorem in this case). This viewpoint allows us to give a new proof of a recent theorem of Billerey and Menares. We end with some examples, including where p=2 and ℓ is a Mersenne prime.
Iaith wreiddiol | Saesneg |
---|---|
Tudalennau (o-i) | 248-261 |
Nifer y tudalennau | 14 |
Cyfnodolyn | Journal of Number Theory |
Cyfrol | 143 |
Dyddiad ar-lein cynnar | 4 Meh 2014 |
Dynodwyr Gwrthrych Digidol (DOIs) | |
Statws | Cyhoeddwyd - Hyd 2014 |
Cyhoeddwyd yn allanol | Ie |