LARGE FOURIER COEFFICIENTS OF HALF-INTEGER WEIGHT MODULAR FORMS

被引：0

作者：

Gun, S. ^{[1
]}

Kohnen, W. ^{[2
]}

Soundararajan, K. ^{[3
]}

机构：

[1] HBNI, Inst Math Sci, CIT Campus, Chennai 600113, India

[2] Heidelberg Univ, Math Inst, Neuenheimer Feld 205, D-69120 Heidelberg, Germany

[3] Stanford Univ, 450 Jane Stanford Way, Bldg 380, Stanford, CA 94305 USA

来源：

AMERICAN JOURNAL OF MATHEMATICS | 2024年 / 146卷 / 04期

关键词：

EXTREME VALUES; TWISTS; SUMS;

D O I：

10.1353/ajm.2024.a932437

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This article is concerned with the Fourier coefficients of cusp forms (not necessarily eigenforms) of half-integer weight lying in the plus space. We give a soft proof that there are infinitely many fundamental discriminants D such that the Fourier coefficients evaluated at D are non-zero. By adapting the resonance method, we also demonstrate that such Fourier coefficients must take quite large values.

引用

页码：1169 / 1191

页数：24