On higher congruences between automorphic forms
Number Theory
2013-02-12 v1
Abstract
We prove a commutative algebra result which has consequences for congruences between automorphic forms modulo prime powers. If C denotes the congruence module for a fixed automorphic Hecke eigenform \pi_0 we prove an exact relation between the p-adic valuation of the order of C and the sum of the exponents of p-power congruences between the Hecke eigenvalues of \pi_0 and other automorphic forms. We apply this result to several situations including the congruences described by Mazur's Eisenstein ideal.
Cite
@article{arxiv.1302.2381,
title = {On higher congruences between automorphic forms},
author = {Tobias Berger and Krzysztof Klosin and Kenneth Kramer},
journal= {arXiv preprint arXiv:1302.2381},
year = {2013}
}
Comments
11 pages