A conjectural extension of Hecke's converse theorem
Number Theory
2019-06-19 v2
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.
Keywords
Cite
@article{arxiv.1704.02570,
title = {A conjectural extension of Hecke's converse theorem},
author = {Sandro Bettin and Jonathan W. Bober and Andrew R. Booker and Brian Conrey and Min Lee and Giuseppe Molteni and Thomas Oliver and David J. Platt and Raphael S. Steiner},
journal= {arXiv preprint arXiv:1704.02570},
year = {2019}
}
Comments
21 pages, to appear in The Ramanujan Journal