Rigorous computation of Maass cusp forms of squarefree level

Andrei Seymour-Howell

doi:10.1007/s40993-022-00393-y

Rigorous computation of Maass cusp forms of squarefree level

Andrei Seymour-Howell

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

1 Citation (Scopus)

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.

Original language	English
Article number	83
Number of pages	15
Journal	Research in Number Theory
Volume	8
DOIs	https://doi.org/10.1007/s40993-022-00393-y
Publication status	Published - 8 Oct 2022

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Dataset of Maass forms of squarefree level computed via the Trace Formula
Seymour-Howell, A. (Creator), Zenodo, 23 Sept 2022
DOI: 10.5281/zenodo.7105773, https://zenodo.org/record/7105773
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AB - 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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DO - 10.1007/s40993-022-00393-y

M3 - Article (Academic Journal)

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JO - Research in Number Theory

JF - Research in Number Theory

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Rigorous computation of Maass cusp forms of squarefree level

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Dataset of Maass forms of squarefree level computed via the Trace Formula

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