Convergence to the Plancherel measure of Hecke Eigenvalues
Number Theory
2022-01-11 v1 Probability
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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Cite
@article{arxiv.2201.03523,
title = {Convergence to the Plancherel measure of Hecke Eigenvalues},
author = {Peter Sarnak and Nina Zubrilina},
journal= {arXiv preprint arXiv:2201.03523},
year = {2022}
}
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17 pages