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arXiv · 1509.04835

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

Marcus du Sautoy
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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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Marcus du Sautoy. 2015-09-16. Natural boundaries for Euler products of Igusa zeta functions of elliptic curves. https://arxiv.org/abs/1509.04835

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