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

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.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1142/S1793042118501415

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
World Scientific Publishing Publisher's website
Journal:
International Journal of Number Theory Journal website
Volume:
14
Issue:
8
Pages:
2317-2331
Publication date:
2018-07-03
Acceptance date:
2018-03-26
DOI:
EISSN:
1793-7310
ISSN:
1793-0421
Source identifiers:
860007
Language:
English
Keywords:
Pubs id:
pubs:860007
UUID:
uuid:87314b4b-e680-48f0-b6e1-84da6b4731bd
Local pid:
pubs:860007
Deposit date:
2018-06-30

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