Rankin-Selberg coefficients in large arithmetic progressions  

作　　者：Emmanuel Kowalski Yongxiao Lin Philippe Michel 

机构地区：[1]Department of Mathematics,ETH Zurich,Zurich CH-8092,Switzerland [2]Data Science Institute,Shandong University,Jinan 250100,China [3]EPFL/MATH/TAN,Lausanne CH-1015,Switzerland

出　　处：《Science China Mathematics》2023年第12期2767-2778,共12页中国科学：数学（英文版）

基　　金：supported by the SNF(Grant No.200021_197045)。

摘　　要：Let(λ_f(n))_(n≥1)be the Hecke eigenvalues of either a holomorphic Hecke eigencuspform or a Hecke-Maass cusp form f.We prove that,for any fixedη>0,under the Ramanujan-Petersson conjecture for GL_(2)Maass forms,the Rankin-Selberg coefficients(λ_f(n)^(2))_(n≥1)admit a level of distributionθ=2/5+1/260-ηin arithmetic progressions.

关 键 词：arithmetic progressions Rankin-Selberg L-functions δ-method 

分 类 号：O174[理学—数学]