Convergence to the Plancherel measure of Hecke eigenvalues

Peter Sarnak; Nina Zubrilina

doi:10.4064/aa230419-4-10

Convergence to the Plancherel measure of Hecke eigenvalues

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	191-213
Number of pages	23
Journal	Acta Arithmetica
Volume	214
DOIs	https://doi.org/10.4064/aa230419-4-10
State	Published - 2024
Externally published	Yes

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Keywords

Hecke eigenvalues
Plancherel measure
eigenvalue distribution
modular curve

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10.4064/aa230419-4-10

Cite this

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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{\textquoteright}s problem of bounding the multiplicities of modular forms whose coefficients lie in number fields of degree d.",

keywords = "Hecke eigenvalues, Plancherel measure, eigenvalue distribution, modular curve",

author = "Peter Sarnak and Nina Zubrilina",

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T1 - Convergence to the Plancherel measure of Hecke eigenvalues

AU - Sarnak, Peter

AU - Zubrilina, Nina

N1 - Publisher Copyright: © Instytut Matematyczny PAN, 2024.

PY - 2024

Y1 - 2024

N2 - 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.

AB - 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.

KW - Hecke eigenvalues

KW - Plancherel measure

KW - eigenvalue distribution

KW - modular curve

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EP - 213

JO - Acta Arithmetica

JF - Acta Arithmetica

ER -

Convergence to the Plancherel measure of Hecke eigenvalues

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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