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 

机构地区：[1]Department of Mathematics,The University of Hong Kong,Hong Kong,China [2]Department of Mathematics,The Chinese University of Hong Kong,Hong Kong,China [3]Institute of Modern Mathematics,School of Mathematics and Statistics,Henan University,Kaifeng 475004,China [4]Shenzhen Key Laboratory of Advanced Machine Learning and Applications,College of Mathematics and Statistics,Shenzhen University,Shenzhen 518060,China

出　　处：《Science China Mathematics》2021年第11期2381-2394,共14页中国科学：数学（英文版）

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)。

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

关 键 词：automorphic representation Hecke eigenvalue Maass cusp form sign change 

分 类 号：O174[理学—数学]