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A CONVERSE THEOREM WITHOUT ROOT NUMBERS

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  21 May 2019

Andrew R. Booker
Andrew R. Booker*
Affiliation:
Howard House, University of Bristol, Queen’s Avenue, Bristol BS8 1SN, U.K. email andrew.booker@bristol.ac.uk
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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.

MSC classification

Primary: 11F11: Holomorphic modular forms of integral weight 11F66: Langlands $L$-functions; one variable Dirichlet series and functional equations
Type
Research Article
Information
Mathematika , Volume 65 , Issue 4 , 2019 , pp. 862 - 873
Copyright
Copyright © University College London 2019 

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Footnotes

The author was partially supported by EPSRC Grant EP/K034383/1.

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