Congruences between modular forms: raising the level and dropping Euler factors.

Abstract:

:We discuss the relationship among certain generalizations of results of Hida, Ribet, and Wiles on congruences between modular forms. Hida's result accounts for congruences in terms of the value of an L-function, and Ribet's result is related to the behavior of the period that appears there. Wiles' theory leads to a class number formula relating the value of the L-function to the size of a Galois cohomology group. The behavior of the period is used to deduce that a formula at "nonminimal level" is obtained from one at "minimal level" by dropping Euler factors from the L-function.

authors

Diamond F

doi

10.1073/pnas.94.21.11143

keywords:

subject

Has Abstract

pub_date

1997-10-14 00:00:00

pages

11143-6

issue

21

eissn

0027-8424

issn

1091-6490

journal_volume

94

pub_type

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