WebWeil’s converse theorem for Maass forms and cancellation of zeros Michael Neururer, Thomas D Oliver Mathematics Acta Arithmetica 2024 We first prove a new converse theorem for Dirichlet series of Maass type which does not assume an Euler product. The underlying idea is a geometric generalisation of Weil's classical argument. By… 10 PDF WebFirstly, 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 ...
Koecher-Maass series associated to Hermitian modular
Web13 dec. 2024 · Our goal is converse theorems for automorphic distributions and Maass forms of level N characterizing them by analytic properties of the associated L-functions. As an application of our... Web23 ian. 2024 · I found that one may need converse theorem for Rankin-Selberg $L$-functions, which seems intractable. I also tried to directly construct the candidate … round engine
ConversetheoremsforautomorphicdistributionsandMaass …
WebA Converse Theorem and the Saito-Kurokawa Lift 353 Proof. The functional equation in the case kD0 is found by computing the scattering matrix in [Iw;Theorem 6.5]. The functional equation for general even k<0 is deduced from this by successively applying the Maass operator LkD¡iy@xCy@y¡k=2;since L¡kE ¡kD(sCk=2)E¡k¡2. Web18 sept. 2024 · Two converse theorems for Maass forms September 2024 Authors: Michael Neururer Thomas Oliver Teesside University Preprints and early-stage research may not have been peer reviewed yet. Abstract... WebA converse theorem for Maass forms of weight = 0 under this weaker assumptions is obtained in Neururer and Oliver [23], which appeared very recently in the final stage of … round engine round up 2021