Hypergeometric functions over ${\mathbb {F}_p}$ and relations to elliptic curves and modular forms
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Publication:3402163
DOI10.1090/S0002-9939-09-10068-0zbMATH Open1222.11058arXiv0805.2885MaRDI QIDQ3402163
Author name not available (Why is that?)
Publication date: 2 February 2010
Published in: (Search for Journal in Brave)
Abstract: For 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.
Full work available at URL: https://arxiv.org/abs/0805.2885
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