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arXiv · 2201.03523

Convergence to the Plancherel measure of Hecke Eigenvalues

Peter Sarnak·Nina Zubrilina
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Abstract

We give improved uniform estimates for the rate of convergence to Plancherel measure of Hecke eigenvalues of holomorphic forms of weight 2 and level N. These are applied to determine the sharp cutoff for the non-backtracking random walk on arithmetic Ramanujan graphs and to Serre's problem of bounding the multiplicities of modular forms whose coefficients lie in number fields of degree d.

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Peter Sarnak, Nina Zubrilina. 2022-01-10. Convergence to the Plancherel measure of Hecke Eigenvalues. https://arxiv.org/abs/2201.03523

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