Congruences of modular forms and Selmer groups
نویسندگان
چکیده
منابع مشابه
Congruences between Selmer groups ∗
The study of congruences between arithmetically interesting numbers has a long history and plays important roles in several areas of number theory. Examples of such congruences include the Kummer congruences between Bernoulli numbers and congruences between coefficients of modular forms. Many of these congruences could be interpreted as congruences between special values of L-functions of arith...
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We prove two congruences for the coefficients of power series expansions in t of modular forms where t is a modular function. As a result, we settle two recent conjectures of Chan, Cooper and Sica. Additionally, we provide tables of congruences for numbers which appear in similar power series expansions and in the study of integral solutions of Apéry-like differential equations.
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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...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2001
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2001.v8.n4.a8