Ramanujan-style congruences of local origin

Neil Dummigan*, Daniel Fretwell

*Awdur cyfatebol y gwaith hwn

Allbwn ymchwil: Cyfraniad at gyfnodolynErthygladolygiad gan gymheiriaid

8 Dyfyniadau (Scopus)

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 wreiddiolSaesneg
Tudalennau (o-i)248-261
Nifer y tudalennau14
CyfnodolynJournal of Number Theory
Cyfrol143
Dyddiad ar-lein cynnar4 Meh 2014
Dynodwyr Gwrthrych Digidol (DOIs)
StatwsCyhoeddwyd - Hyd 2014
Cyhoeddwyd yn allanolIe

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