On higher congruences between automorphic forms
نویسندگان
چکیده
منابع مشابه
On Higher Congruences between Automorphic Forms
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 π0 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 π0 and other automorphic forms. We a...
متن کاملHigher congruences between modular forms
It is well-known that two modular forms on the same congruence subgroup and of the same weight, with coefficients in the integer ring of a number field, are congruent modulo a prime ideal in this integer ring, if the first B coefficients of the forms are congruent modulo this prime ideal, where B is an effective bound depending only on the congruence subgroup and the weight of the forms. In thi...
متن کاملHigher Congruences Between Modular Forms
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متن کاملAutomorphic forms of higher order
In this paper a theory of Hecke operators for higher order modular forms is established. The definition of higher order forms is extended beyond the realm of parabolic invariants. A canonical inner product is introduced. The role of representation theoretic methods is clarified and, motivated by higher order forms, new convolution products of L-functions are introduced.
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2014
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2014.v21.n1.a5