On the first negative Hecke eigenvalue of an automorphic representation of GL_(2)(A_(Q))

作     者：Yuk-Kam Lau Ming Ho Ng Hengcai Tang Yingnan Wang Yuk-Kam Lau;Ming Ho Ng;Hengcai Tang;Yingnan Wang

作者机构：Department of MathematicsThe University of Hong KongHong KongChina Department of MathematicsThe Chinese University of Hong KongHong KongChina Institute of Modern MathematicsSchool of Mathematics and StatisticsHenan UniversityKaifeng 475004China Shenzhen Key Laboratory of Advanced Machine Learning and ApplicationsCollege of Mathematics and StatisticsShenzhen UniversityShenzhen 518060China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2021年第64卷第11期

页      面：2381-2394页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by General Research Fund of the Research Grants Council of Hong Kong(Grant Nos.17313616 and 17305617) supported by National Natural Science Foundation of China(Grant No.11871193) the Program for Young Scholar of Henan Province(Grant No.2019GGJS026) supported by National Natural Science Foundation of China(Grant No.11871344) 

主　　题：automorphic representation Hecke eigenvalue Maass cusp form sign change 

摘      要：Letπbe a self-dual irreducible cuspidal automorphic representation of GL_(2)(A_(Q))with trivial central *** Hecke eigenvalue λπ(n)is a real multiplicative function in *** show that λπ(n)0 for some nQ^(2/5)_(π),where Qπdenotes(a special value of)the analytic *** value 2/5 is the first explicit exponent for Hecke-Maass newforms.