A conjectural extension of Hecke's converse theorem

Sandro Bettin, Jonathan Bober, Andrew Booker, Brian Conrey, Min Lee, Thomas Oliver, David Platt, Raphael Steiner

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)659-684
Number of pages24
JournalRamanujan Journal
Issue number3
Publication statusPublished - 10 Nov 2017


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