Gaussian Hypergeometric Evaluations of Traces of Frobenius for Elliptic\n Curves

2010/03/23 by Catherine Lennon, Lennon, Catherine
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications

paper · pdf · doi:10.48550/arxiv.1003.4421

Abstract

We present here a formula for expressing the trace of the Frobenius\nendomorphism of an elliptic curve E over mathbbF_q satisfying j(E)\≠\n0,1728 and q\≡ 1 pmod12 in terms of special values of Gaussian\nhypergeometric series. This paper uses methods introduced in Fuselier's work\nfor one parameter families of curves to express the trace of Frobenius of E\nas a function of its j-invariant and discriminant instead of a parameter,\nwhich are more intrinsic characteristics of the curve.\n

Citations

• A Trace Formula for Certain Hecke Operators and Gaussian Hypergeometric Functions

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