Hybrid sup-norm bounds for Hecke-Maass cusp forms

被引：25

作者：

Templier, Nicolas ^{[1
]}

机构：

[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2015年 / 17卷 / 08期

基金：

美国国家科学基金会;

关键词：

Automorphic forms; trace formula; amplification; diophantine approximation; EIGENFUNCTIONS;

D O I：

10.4171/JEMS/550

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let f be a Hecke-Maass cusp form of eigenvalue lambda and square-free level N. Normalize the hyperbolic measure so that vol (Y-0(N)) = 1 and the form f such that parallel to f parallel to(2) = 1. It is shown that parallel to f parallel to(infinity) <<epsilon lambda(5/24+epsilon) N1/3+epsilon for all epsilon > 0. This generalizes simultaneously the current best bounds in the eigenvalue and level aspects.

引用

页码：2069 / 2082

页数：14

共 50 条

[41] The twisted second moment of L-functions associated to Hecke-Maass forms
Liu, Sheng-Chi
Streipel, Jakob
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2024, 20 (03) : 849 - 866
[42] Determination of GL(3) Hecke-Maass forms from twisted central values
Munshi, Ritabrata
Sengupta, Jyoti
JOURNAL OF NUMBER THEORY, 2015, 148 : 272 - 287
[43] Central value of the symmetric square L-functions related to Hecke-Maass forms
Tang, Hengcai
Xu, Zhao
LITHUANIAN MATHEMATICAL JOURNAL, 2016, 56 (02) : 251 - 267
[44] Quantitative Quantum Ergodicity and the Nodal Domains of Hecke–Maass Cusp Forms
Junehyuk Jung
Communications in Mathematical Physics, 2016, 348 : 603 - 653
[45] On sup-norm bounds part II: GL(2) Eisenstein series
Assing, Edgar
FORUM MATHEMATICUM, 2019, 31 (04) : 971 - 1006
[46] SHIFTED CONVOLUTION SUM OF d3 AND THE FOURIER COEFFICIENT OF HECKE-MAASS FORMS
Tang, Hengcai
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2015, 92 (02) : 195 - 204
[47] Mean value theorem connected with Fourier coefficients of Hecke-Maass forms for SL(m, Z)
Jiang, Yujiao
Lu, Guangshi
Yan, Xiaofei
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2016, 161 (02) : 339 - 356
[48] A SHIFTED CONVOLUTION SUM OF d3 AND THE FOURIER COEFFICIENTS OF HECKE-MAASS FORMS II
Tang, Hengcai
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2020, 101 (03) : 401 - 414
[49] The cubic moment of Hecke–Maass cusp forms and moments of L-functions
Bingrong Huang
Mathematische Annalen, 2024, 389 : 899 - 945
[50] Odd and even Maass cusp forms for Hecke triangle groups, and the billiard flow
Pohl, Anke D.
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2016, 36 : 142 - 172

← 1 2 3 4 5 →