Rigorous computation of Maass cusp forms of squarefree level

2022/01/21 by Andrei Seymour-Howell, Seymour-Howell, Andrei · 1 citation
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #Advanced Mathematical Identities

paper · pdf · doi:10.48550/arxiv.2201.08760

Abstract

We derive an algorithm to rigorously compute and verify Maass cusp forms of squarefree level and trivial character. The main tool we use is an explicit version of the Selberg trace formula with Hecke operators due to Strömbergsson. We use this algorithm to compute several thousand Maass forms for a range of levels and use this data to obtain numerical evidence towards various conjectures.

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