On Atkin and Swinnerton-Dyer congruence relations (2)

A. O.L. Atkin, Wen Ching Winnie Li, Ling Long

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Abstract

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 eigenforms. 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.

Original languageEnglish (US)
Pages (from-to)335-358
Number of pages24
JournalMathematische Annalen
Volume340
Issue number2
DOIs
StatePublished - Feb 2008

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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