Natural boundaries for Euler products of Igusa zeta functions of elliptic curves

2015/09/16 by Marcus du Sautoy, Sautoy, Marcus du
Mathematics · #11M41 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1509.04835

openalex publication_date 2015/09/16 · openalex created_date 2023/02/16 · openalex updated_date 2026/07/28

Abstract

We study the analytic behaviour of adelic versions of Igusa integrals given by integer polynomials defining elliptic curves. By applying results on the meromorphic continuation of symmetric power L-functions and the Sato-Tate conjectures we prove that these global Igusa zeta functions have some meromorphic continuation until a natural boundary beyond which no continuation is possible.

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