Hypergeometric functions over F_p and relations to elliptic curves and modular forms

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dc.creatorFuselier, Jenny G.
dc.date2008-05-19
dc.date.accessioned2026-07-07T09:39:43Z
dc.date.available2026-07-07T09:39:43Z
dc.descriptionFor primes p congruent to 1 mod 12, we present an explicit relation between the traces of Frobenius on a family of elliptic curves with j-invariant 1728/t and values of a particular 2F1-hypergeometric function over F_p. Additionally, we determine a formula for traces of Hecke operators T_k(p) on spaces of cusp forms of weight k and level 1 in terms of the same traces of Frobenius. This leads to formulas for Ramanujan's tau-function in terms of hypergeometric functions.
dc.description26 pages
dc.identifierhttps://arxiv.org/abs/0805.2885
dc.identifierhttp://arxiv.org/abs/0805.2885
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161274
dc.subjectNumber Theory
dc.subject11F30 (Primary) 11T24, 11G20, 33C99 (Secondary)
dc.titleHypergeometric functions over F_p and relations to elliptic curves and modular forms
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