On Atkin and Swinnerton-Dyer congruences for noncongruence modular forms
نویسندگان
چکیده
منابع مشابه
Modular Forms on Noncongruence Subgroups and Atkin-Swinnerton-Dyer Relations
This is a joint project with Liqun Fang Ben Linowitz Andrew Rupinski Helena Verrill We give new examples of modular forms on noncongruence subgroups whose l-adic representations are modular and whose expansion coefficients satisfy Atkin-Swinnerton-Dyer congruences.
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In this paper we give an example of a noncongruence subgroup whose three-dimensional space of cusp forms of weight 3 has the following properties. For each of the four residue classes of odd primes modulo 8 there is a basis whose Fourier coefficients at infinity satisfy a three-term Atkin and Swinnerton-Dyer congruence relation, which is the p-adic analogue of the threeterm recursion satisfied ...
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We derive the Atkin–Swinnerton–Dyer partition congruences for the modulus 11 by use of Winquist’s identity. Classification: 11P83
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In the previous two papers with the same title ([LLY05] by W.C. Li, L. Long, Z. Yang and [ALL05] by A.O.L. Atkin, W.C. Li, L. Long), the authors have studied special families of cuspforms for noncongruence arithmetic subgroups. It was found that the Fourier coefficients of these modular forms at infinity satisfy three-term Atkin and Swinnerton-Dyer congruence relations which are the p-adic anal...
متن کاملOn Atkin and Swinnerton-dyer Congruence Relations (2)
In this paper we give an example of a noncongruence subgroup whose three-dimensional space of cusp forms of weight 3 has the following properties. For each of the four residue classes of odd primes modulo 8 there is a basis whose Fourier coefficients at infinity satisfy a three-term Atkin and Swinnerton-Dyer congruence relation, which is the p-adic analogue of the threeterm recursion satisfied ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2014
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2014-12162-9