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A conjectural extension of Hecke’s converse theorem

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)659-684
Number of pages26
JournalRamanujan Journal
Volume47
Issue number3
Early online date10 Nov 2017
DOIs
DateSubmitted - 9 Apr 2017
DateAccepted/In press - 16 Aug 2017
DateE-pub ahead of print - 10 Nov 2017
DatePublished (current) - Dec 2018

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.

    Research areas

  • Modular forms, Converse theorems, Ramanujan sums

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    Rights statement: This is the final published version of the article (version of record). It first appeared online via Springer at https://link.springer.com/article/10.1007%2Fs11139-017-9953-y . Please refer to any applicable terms of use of the publisher.

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    Licence: CC BY

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