Bounds for Average toward the Resonance Barrier for GL(3)×GL(2)Automorphic Forms  

作　　者：Huan Qin Yang Bo Ye 

机构地区：[1]San Diego State University—Imperial Valley,Calexico,CA,92231,USA [2]Department of Mathematics,The University of Iowa,Iowa City,Iowa,52242-1419,USA

出　　处：《Acta Mathematica Sinica,English Series》2023年第9期1667-1683,共17页数学学报（英文版）

摘　　要：Let f be a fixed Maass form for SL_3(Z)with Fourier coefficients A_(f)(m,n).Let g be a Maass cusp form for SL_2(G)with Laplace eigenvalue(1/4)+k^(2) and Fourier coefficientλ_(g)(n),or a holomorphic cusp form of even weight k.Denote by S_(X)(f×g,α,β)a smoothly weighted sum of A_(f)(1,n)λ_(g)(n)e(αn~β)for X 0 are fixed real numbers.The subject matter of the present paper is to prove non-trivial bounds for a sum of S_(X)(f×g,α,β)over g as k tends to∞with X.These bounds for average provide insight for the corresponding resonance barriers toward the Hypothesis S as proposed by Iwaniec,Luo,and Sarnak.

关 键 词：Maass cusp form holomorphic cusp form Hypothesis S resonance barrier Kuznetsov trace formula Petersson's formula Voronoi's summation formula 

分 类 号：O174[理学—数学]