Robert Pollack, Tom Weston
Published 2005-08-30Version 1
We prove a formula (analogous to that of Kida in classical Iwasawa theory and generalizing that of Hachimori-Matsuno for elliptic curves) giving the analytic and algebraic p-adic Iwasawa invariants of a modular eigenform over an abelian p-extension of Q to its p-adic Iwasawa invariants over Q. On the algebraic side our methods, which make use of congruences between modular forms, yield a Kida-type formula for a very general class of ordinary Galois representations. We are further able to deduce a Kida-type formula for elliptic curves at supersingular primes.
Congruences satisfied by eta-quotients
Congruences involving $\binom{2k}k^2\binom{4k}{2k}m^{-k}$
Congruences involving $\binom{2k}k^2\binom{3k}km^{-k}$
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