{"title":"Cancellation in the additive twists of Fourier coefficients for GL2 and GL3 over number fields","authors":"Zhi Qi","doi":"10.1353/ajm.2019.0034","DOIUrl":null,"url":null,"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.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2019-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1353/ajm.2019.0034","citationCount":"10","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"American Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1353/ajm.2019.0034","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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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