Journal article

Weil's converse theorem for Maass forms and cancellation of zeros

Abstract:
We prove two principal results. Firstly, we characterise Maass forms in terms of functional equations for Dirichlet series twisted by primitive characters. The key point is that the twists are allowed to be meromorphic. This weakened analytic assumption applies in the context of our second theorem, which shows that the quotient of the symmetric square L-function of a Maass newform and the Riemann zeta function has infinitely many poles.
Publication status:
Published
Peer review status:
Peer reviewed

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Files:
• (Accepted manuscript, 522.7KB)
Publisher copy:
10.4064/aa190811-3-2

Authors

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Polskiej Akademii Nauk, Instytut Matematyczny Publisher's website
Journal:
Acta Arithmetica Journal website
Volume:
196
Issue:
4
Pages:
387-422
Publication date:
2020-07-11
Acceptance date:
2020-01-31
DOI:
EISSN:
1730-6264
ISSN:
0065-1036
Keywords:
Pubs id:
1084456
Local pid:
pubs:1084456
Deposit date:
2020-02-03