A conjectural extension of Hecke's converse theorem

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

A conjectural extension of Hecke's converse theorem

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

SCEDT Engineering

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	659-684
Number of pages	24
Journal	Ramanujan Journal
Volume	47
Issue number	3
Publication status	Published - 10 Nov 2017

Access to Document

https://link.springer.com/article/10.1007%2Fs11139-017-9953-yLicence: CC BY

Cite this

@article{fc6b7bca937c41fea0d1894af32f424f,

title = "A conjectural extension of Hecke's converse theorem",

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.",

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

year = "2017",

month = nov,

day = "10",

language = "English",

volume = "47",

pages = "659--684",

journal = "Ramanujan Journal",

issn = "1382-4090",

publisher = "Springer Netherlands",

number = "3",

}

TY - JOUR

T1 - A conjectural extension of Hecke's converse theorem

AU - Bettin, Sandro

AU - Bober, Jonathan

AU - Booker, Andrew

AU - Conrey, Brian

AU - Lee, Min

AU - Oliver, Thomas

AU - Platt, David

AU - Steiner, Raphael

PY - 2017/11/10

Y1 - 2017/11/10

N2 - 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.

AB - 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.

M3 - Article

SN - 1382-4090

VL - 47

SP - 659

EP - 684

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 3

ER -

A conjectural extension of Hecke's converse theorem

Abstract

Access to Document

Fingerprint

Cite this