Hypergeometric functions over mathbbF_q and traces of Frobenius for\n elliptic curves

2012/08/02 by Rupam Barman, Barman, Rupam, Gautam Kalita +1
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.1208.0508

Abstract

We present here explicit relations between the traces of Frobenius\nendomorphisms of certain families of elliptic curves and special values of\n₂F₁-hypergeometric functions over mathbbF_q for q \≡ 1\n(\mod 6) and q \≡ 1 (\mod 4).\n

Related

• Hypergeometric functions over F_p and relations to elliptic curves and modular forms
• Gaussian Hypergeometric Evaluations of Traces of Frobenius for Elliptic\n Curves
• p-Adic hypergeometric functions and the trace of Frobenius of elliptic curves
• Hyperelliptic curves over \mathbbF_q and Gaussian hypergeometric series
• Hypergeometric functions and algebraic curves y^e=x^d+ax+b