A conjectural extension of Hecke’s converse theorem

Bettin, S., Bober, J., Booker, A., Conrey, B., Lee, M., Molteni, G., Oliver, T., Platt, D. and Steiner, R. 2018. A conjectural extension of Hecke’s converse theorem. The Ramanujan Journal. 47, pp. 659-684. https://doi.org/10.1007/s11139-017-9953-y

TitleA conjectural extension of Hecke’s converse theorem
TypeJournal article
AuthorsBettin, S., Bober, J., Booker, A., Conrey, B., Lee, M., Molteni, G., Oliver, T., Platt, D. and Steiner, R.
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.

JournalThe Ramanujan Journal
Journal citation47, pp. 659-684
ISSN1572-9303
1382-4090
Year2018
PublisherSpringer
Publisher's version
License
CC BY 4.0
File Access Level
Open (open metadata and files)
Digital Object Identifier (DOI)https://doi.org/10.1007/s11139-017-9953-y
Web address (URL)https://link.springer.com/article/10.1007/s11139-017-9953-y
Publication dates
Published online10 Nov 2017
Published in printDec 2018

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