Convergence to the Plancherel measure of Hecke eigenvalues

Peter Sarnak, Nina Zubrilina

Type: Article

Publication Date: 2024-01-01

Citations: 0

DOI: https://doi.org/10.4064/aa230419-4-10

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

Locations

Acta Arithmetica - View - PDF
arXiv (Cornell University) - View - PDF
Acta Arithmetica - View - PDF
arXiv (Cornell University) - View - PDF
Acta Arithmetica - View - PDF
arXiv (Cornell University) - View - PDF

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Works Cited by This (13)

Action	Title	Year	Authors
+	Statistical Properties of Eigenvalues of the Hecke Operators	1987	Peter Sarnak
+ PDF	The distribution of the eigenvalues of Hecke operators	1997	J. Brian Conrey William Duke David W. Farmer
+ PDF	A Large Sieve Inequality of Elliott-Montgomery-Vaughan Type for Automorphic Forms and Two Applications	2008	Yuk-Kam Lau Jie Wu
+	Effective equidistribution of eigenvalues of Hecke operators	2008	M. Ram Murty Kaneenika Sinha
+ PDF Chat	Low lying zeros of families of L-functions	2000	Henryk Iwaniec Wenzhi Luo Peter Sarnak
+	The second moment of the symmetric square $L$-functions	2001	Henryk Iwaniec Philippe Michel
+	Families of Ramanujan graphs and quaternion algebras	2009	Denis Charles Eyal Z. Goren Kristin Lauter
+ PDF Chat	Bounds for traces of Hecke operators and applications to modular and elliptic curves over a finite field	2018	Ian Petrow
+ PDF Chat	Vanishing Fourier coefficients of Hecke eigenforms	2021	Frank Calegari Naser T. Sardari
+	Prime geodesic theorem.	1984	Henryk Iwaniec