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

Michael Neururer, Thomas Oliver

Research output: Contribution to journalArticlepeer-review


We prove two principal results. Firstly, we characterise Maass forms in terms of functional equations for Dirichlet series twisted by primitive characters. The key point is that the twists are allowed to be meromorphic. This weakened analytic assumption applies in the context of our second theorem, which shows that the quotient of the symmetric square L-function of a Maass newform and the Riemann zeta function has infinitely many poles.
Original languageEnglish
Pages (from-to)387-422
Number of pages35
JournalActa Arithmetica
Issue number4
Publication statusPublished - 11 Jul 2020


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