A converse theorem without root numbers

Abstract

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.

10 pages, to appear in Mathematika

References in corpus (1)

• A conjectural extension of Hecke's converse theorem

Cited by in corpus (1)

• Weil's converse theorem for Maass forms and cancellation of zeros