A conjectural extension of Hecke’s converse theorem : WestminsterResearch

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Title	A conjectural extension of Hecke’s converse theorem
Type	Journal article
Authors	Bettin, 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.
Journal	The Ramanujan Journal
Journal citation	47, pp. 659-684
ISSN	1572-9303
	1382-4090
Year	2018
Publisher	Springer
Publisher's version	published-conjectural-hecke.pdf 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
Published online	10 Nov 2017
Published in print	Dec 2018

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A conjectural extension of Hecke’s converse theorem

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