### Numerical verification of Maass cusp forms

Linfoot Number Theory Seminar

21st April 2021, 11:00 am – 12:00 pm

Fry Building, Online

A well-known algorithm for computing the Laplace eigenvalue of Maass cusp forms is due to Hejhal from the 1990's, however this relies on a heuristic argument and thus doesn't certify the correctness of the values. In this talk I will describe a method to numerically certify the Laplace eigenvalue of Maass cusp forms of square-free level and trivial character. This method relies on an explicit version of the Selberg trace formula that includes Hecke operators. In addition, I will show how this method can be used the compute the Laplace eigenvalues in the first place.

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