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

Author: 

du Sautoy, M

Publication Date: 

3 July 2018

Journal: 

International Journal of Number Theory

Last Updated: 

2021-06-12T08:52:20.67+01:00

Issue: 

8

Volume: 

14

DOI: 

10.1142/S1793042118501415

page: 

2317-2331

abstract: 

We study the analytic behavior 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.

Symplectic id: 

860007

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article