We answer a challenge posed in (Math. Ann. 363 (2015), no. 1-2, 423-454) by
proving a version of Weil's converse theorem that assumes a functional equation
for character twists but allows their root numbers to vary arbitrarily.Comment: 10 pages, to appear in Mathematik

Booker, Andrew R.

English

arXiv

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.</p

A converse theorem without root numbers

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