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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
Issue number3
Early online date10 Nov 2017
DateSubmitted - 9 Apr 2017
DateAccepted/In press - 16 Aug 2017
DateE-pub ahead of print - 10 Nov 2017
DatePublished (current) - Dec 2018


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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    Licence: CC BY


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