Cancellation in the additive twists of Fourier coefficients for GL2 and GL3 over number fields

IF 1.7 1区数学 Q1 MATHEMATICS

American Journal of Mathematics Pub Date : 2019-09-06 DOI:10.1353/ajm.2019.0034

Zhi Qi

引用次数: 10

Abstract

abstract:In this article, we study the sum of additively twisted Fourier coefficients of an irreducible cuspidal automorphic representation of ${\rm GL}_2$ or ${\rm GL}_3$ over an arbitrary number field. When the representation is unramified at all non-archimedean places, we prove the Wilton type bound for ${\rm GL}_2$ and the Miller type bound for ${\rm GL}_3$ which are uniform in terms of the additive character.

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GL2和GL3的傅立叶系数在数域上的加性扭曲抵消

文摘：在本文中，我们研究了任意数域上${\rm-GL}_2$或${\rm-GL}_3$的不可约尖自同构表示的加扭傅立叶系数的和。当表示在所有非阿基米德位置上都是非分枝的时，我们证明了$｛\rm GL｝_2$的Wilton型界和$｛\ rm GL｝_3$的Miller型界在可加性方面是一致的。

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

American Journal of Mathematics 数学-数学

CiteScore

3.20

自引率

0.00%

发文量

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.