A converse theorem without root numbers

Andrew Booker

doi:10.1112/S0025579319000184

A converse theorem without root numbers

Andrew Booker^*

^*Corresponding author for this work

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Abstract

We answer a challenge posed in Booker [L-functions as distributions. Math. Ann. 363(1-2) (2015), 423-454, §1.3] by proving a version of Weil's converse theorem [Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann. 168 (1967), 149-156] that assumes a functional equation for character twists but allows their root numbers to vary arbitrarily.

Original language	English
Pages (from-to)	862-873
Number of pages	12
Journal	Mathematika
Volume	65
Issue number	4
DOIs	https://doi.org/10.1112/S0025579319000184
Publication status	Published - 21 May 2019

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A converse theorem without root numbers

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