THE QUANTITATIVE DISTRIBUTION OF HECKE EIGENVALUES

Yingnan Wang

Type: Article

Publication Date: 2014-04-10

Citations: 8

DOI: https://doi.org/10.1017/s0004972714000070

Abstract

Abstract In this paper, we prove that the Sato–Tate conjecture for primitive Maass forms holds on average. We also investigate the rate of convergence in the Sato–Tate conjecture and establish some estimates of the discrepancy with respect to the Sato–Tate measure on the average of primitive Maass forms.

Locations

Bulletin of the Australian Mathematical Society - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	The quantitative distribution of Hecke eigenvalues of Maass forms	2022	Moni Kumari Jyoti Sengupta
+ PDF Chat	Fluctuations in the Distribution of Hecke Eigenvalues about the Sato–Tate Measure	2017	Neha Prabhu Kaneenika Sinha
+	Quantitative version of the joint distribution of eigenvalues of the Hecke operators	2011	Yuk-Kam Lau Yingnan Wang
+	Fluctuations in the distribution of Hecke eigenvalues about the Sato-Tate measure	2017	Neha Prabhu Kaneenika Sinha
+	Fluctuations in the distribution of Hecke eigenvalues about the Sato-Tate measure	2017	Neha Prabhu Kaneenika Sinha
+ PDF Chat	Distribution of Hecke eigenvalues	2006	Hirofumi Nagoshi
+	The distribution of the eigenvalues of Hecke operators	1996	J. Brian Conrey William Duke David W. Farmer
+	The distribution of the eigenvalues of Hecke operators	1996	J. Brian Conrey William Duke David W. Farmer
+	Quantitative versions of the joint distributions of Hecke eigenvalues	2016	Hengcai Tang Yingnan Wang
+	The quantitative distribution of Hecke eigenvalues of Maass forms	2022	Moni Kumari Jyoti Sengupta
+ PDF Chat	A Sato–Tate law for GL (3)	2014	Valentin Blomer Jack Buttcane Nicole Raulf
+ PDF Chat	Quantum Variance of Maass-Hecke Cusp Forms	2009	Peng Zhao
+	Statistics of Hecke eigenvalues	2017	YK Lau
+	On the Hecke Eigenvalues of Maass Forms	2014	Wenzhi Luo Zhou Fan
+	The Distribution of the Eigenvalues of Hecke Operators	2006	E. P. Golubeva
+ PDF Chat	The distribution of the eigenvalues of Hecke operators	1997	J. Brian Conrey William Duke David W. Farmer
+	A lower bound for the discrepancy in a Sato-Tate type measure	2023	Jishu Das
+ PDF Chat	On Hecke eigenvalues of Siegel modular forms in the Maass space	2017	Sanoli Gun Biplab Paul Jyoti Sengupta
+	Some notes on distribution of Hecke eigenvalues for Maass cusp forms	2017	Yingnan Wang Xuanxuan Xiao
+	Sato-Tate equidistribution for families of Hecke-Maass forms on SL(n,R)/SO(n)	2015	Jasmin Matz Nicolas Templier

Works That Cite This (8)

Action	Title	Year	Authors
+	Some notes on distribution of Hecke eigenvalues for Maass cusp forms	2017	Yingnan Wang Xuanxuan Xiao
+	Weighted distribution of low-lying zeros of GL(2) L-functions	2018	Andrew Knightly Caroline Reno
+ PDF Chat	Fluctuations in the Distribution of Hecke Eigenvalues about the Sato–Tate Measure	2017	Neha Prabhu Kaneenika Sinha
+	Central limit theorems for elliptic curves and modular forms with smooth weight functions	2019	Stephan Baier Neha Prabhu Kaneenika Sinha
+ PDF Chat	Weighted Distribution of Low-lying Zeros of GL(2) -functions	2018	Andrew Knightly Caroline Reno
+	Statistics of Hecke eigenvalues for GL(𝑛)	2018	Yuk-Kam Lau Ming Ho Ng Yingnan Wang
+	Central limit theorems for elliptic curves and modular forms with smooth weight functions	2019	Stephan Baier Neha Prabhu Kaneenika Sinha
+	Average Bound Toward the Generalized Ramanujan Conjecture and Its Applications on Sato–Tate Laws for <i>GL</i>(<i>n</i>)	2020	Yuk-Kam Lau Ming Ho Ng Yingnan Wang

Works Cited by This (9)

Action	Title	Year	Authors
+	Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂	2002	Henry Kim
+	Note on a Diophantine inequality in several variables	2000	Jeffrey Barton Hugh L. Montgomery Jeffrey D. Vaaler
+ PDF Chat	Distribution of Hecke eigenvalues	2006	Hirofumi Nagoshi
+ PDF Chat	The distribution of the eigenvalues of Hecke operators	1997	J. Brian Conrey William Duke David W. Farmer
+	Calculation of values of 𝐿-functions associated to elliptic curves	1999	Shigeki Akiyama Yoshio Tanigawa
+ PDF Chat	A Family of Calabi–Yau Varieties and Potential Automorphy II	2011	Tom Barnet-Lamb David Geraghty Michael Harris Richard Taylor
+	Quantitative version of the joint distribution of eigenvalues of the Hecke operators	2011	Yuk-Kam Lau Yingnan Wang
+	La conjecture de Weil. I	1974	Pierre Deligne
+ PDF Chat	Some extremal functions in Fourier analysis	1985	Jeffrey D. Vaaler