BOUNDS FOR EIGENFORMS ON ARITHMETIC HYPERBOLIC 3-MANIFOLDS

被引：16

作者：

Blomer, Valentin ^{[1
]}

Harcos, Gergely ^{[2
,3
]}

Milicevic, Djordje ^{[4
]}

机构：

[1] Univ Gottingen, Inst Math, Bunsenstr 3-5, Gottingen, Germany

[2] MTA Alfred Renyi Inst Math, Budapest, Hungary

[3] Cent European Univ, Budapest, Hungary

[4] Bryn Mawr Coll, Dept Math, Bryn Mawr, PA USA

来源：

DUKE MATHEMATICAL JOURNAL | 2016年 / 165卷 / 04期

基金：

欧洲研究理事会; 匈牙利科学研究基金会;

关键词：

AUTOMORPHIC-FORMS; CUSP FORMS; EIGENFUNCTIONS; EQUIDISTRIBUTION; NUMBER; LAPLACIAN; HOMOLOGY; VALUES; NORMS;

D O I：

10.1215/00127094-3166952

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

On a family of arithmetic hyperbolic 3-manifolds of square-free level, we prove an upper bound for the sup-norm of Hecke-Maa beta cusp forms, with a power saving over the local geometric bound simultaneously in the Laplacian eigenvalue and the volume. By a novel combination of Diophantine and geometric arguments in a noncommutative setting, we obtain bounds as strong as the best corresponding results on arithmetic surfaces.

引用

页码：625 / 659

页数：35

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