AAA. O. L. Atkin
A. O. L. Atkin
*This is an algorithmically generated author record based on publicly available information.
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The organizations/institutes from the scholar's latest article
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A. O. L. Atkin has a total of 2 co-authors. Here are the top co-authors by number of shared publications:
- Ling Long
Department of Mathematics, Iowa State University, Ames, Iowa 50011
2 shared publications - Wen-Ching Winnie Li
Department of Mathematics, Pennsylvania State University, University Park, USA
2 shared publications
Latest Publications
- 25 August 2007
- Published by Springer Nature in Mathematische Annalen
- Vol. 340 (2) , 335-358
On Atkin and Swinnerton-Dyer congruence relations (2)
- 25 August 2007
- Published by Springer Nature in Mathematische Annalen
- Vol. 340 (2) , 335-358
On Atkin and Swinnerton-Dyer congruence relations (2)
- Open Access
On 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 three-term recursion satisfied by the coefficients of classical Hecke eigen forms. We also show that there is an automorphic $L$-function over $\mathbb Q$ whose local factors agree with those of the $l$-adic Scholl representations attached to the space of noncongruence cusp forms.Open AccessOn 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 three-term recursion satisfied by the coefficients of classical Hecke eigen forms. We also show that there is an automorphic $L$-function over $\mathbb Q$ whose local factors agree with those of the $l$-adic Scholl representations attached to the space of noncongruence cusp forms.