On the universal p-adic sigma and Weierstrass zeta functions

2019/03/06 by Clifford Blakestad, David M. Grant, Blakestad, Clifford +1
Mathematics · #11G07 (primary) 14G27 (secondary) #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1903.02480

openalex publication_date 2019/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For primes p>3 we produce a new derivation of the universal p-adic sigma function and p-adic Weierstrass zeta functions of Mazur and Tate for ordinary elliptic curves by a method that highlights congruences among coefficients in Laurent expansions of elliptic functions, and works simultaneously for generalized elliptic curves defined by Weierstrass equations.

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