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A CONVERSE THEOREM WITHOUT ROOT NUMBERS
Published online by Cambridge University Press: 21 May 2019
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.
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- Research Article
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- Copyright © University College London 2019
Footnotes
The author was partially supported by EPSRC Grant EP/K034383/1.