Large Fourier coefficients of half-integer weight modular forms

IF 1.7 1区 数学 Q1 MATHEMATICS
S. Gun, W. Kohnen, K. Soundararajan
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引用次数: 0

Abstract

abstract:

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.

半整数权模块形式的大傅里叶系数
摘要:本文关注位于加空间的半整数权的尖顶形式(不一定是特征形式)的傅里叶系数。我们给出了一个软证明,即存在无穷多个基本判别式 $D$,使得在 $|D|$ 处求值的傅里叶系数非零。通过调整共振方法,我们还证明了这些傅里叶系数必须取相当大的值。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
3.20
自引率
0.00%
发文量
35
审稿时长
24 months
期刊介绍: The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.
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