On Atkin and Swinnerton-Dyer Congruence Relations (2)

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dc.creatorAtkin, A. O. L.
dc.creatorLi, Wen-Ching Winnie
dc.creatorLong, Ling
dc.date2005-12-28
dc.date2007-07-01
dc.date.accessioned2026-07-07T09:18:54Z
dc.date.available2026-07-07T09:18:54Z
dc.descriptionIn 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.
dc.descriptionLast version, to appear on Math Annalen
dc.identifierhttps://arxiv.org/abs/math/0512614
dc.identifierhttp://arxiv.org/abs/math/0512614
dc.identifierMathematische Annalen, Volume 340 No. 2 (2008), pp 335-358
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/154196
dc.subjectNumber Theory
dc.subject11F11, 11F33
dc.titleOn Atkin and Swinnerton-Dyer Congruence Relations (2)
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