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A conjectural extension of Hecke’s converse theorem

Abstract:
We formulate a precise conjecture that, if true, extends the converse theorem of Hecke without requiring hypotheses on twists by Dirichlet characters or an Euler product. The main idea is to linearize the Euler product, replacing it by twists by Ramanujan sums. We provide evidence for the conjecture, including proofs of some special cases and under various additional hypotheses.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Publisher copy:
10.1007/s11139-017-9953-y

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Publisher:
Springer US Publisher's website
Journal:
Ramanujan Journal Journal website
Volume:
47
Issue:
3
Pages:
659–684
Publication date:
2017-11-10
Acceptance date:
2017-09-21
DOI:
EISSN:
1572-9303
ISSN:
1382-4090
Pubs id:
pubs:807185
URN:
uri:fc01e6ea-1da9-4750-b5b6-cb9440f952d3
UUID:
uuid:fc01e6ea-1da9-4750-b5b6-cb9440f952d3
Local pid:
pubs:807185

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