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arXiv · 1704.02570

A conjectural extension of Hecke's converse theorem

Sandro Bettin·Jonathan W. Bober·Andrew R. Booker·Brian Conrey·Min Lee·Giuseppe Molteni·Thomas Oliver·David J. Platt·Raphael S. Steiner
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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.

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Sandro Bettin, Jonathan W. Bober, Andrew R. Booker, Brian Conrey, Min Lee, Giuseppe Molteni, Thomas Oliver, David J. Platt, Raphael S. Steiner. 2017-09-27. A conjectural extension of Hecke's converse theorem. https://doi.org/10.1007/s11139-017-9953-y

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