Hybrid subconvexity bounds for twisted L-functions on GL(3)  

作　　者：Bingrong Huang 

机构地区：[1]School of Mathematics,Shandong University,Jinan 250100,China

出　　处：《Science China Mathematics》2021年第3期443-478,共36页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11531008);the Ministry of Education of China(Grant No.IRT 16R43)。

摘　　要：Let q be a large prime, and χ the quadratic character modulo q. Let Φ be a self-dual Hecke-Maass cusp form for SL(3, Z), and uj a Hecke-Maass cusp form for Γ0(q) ■ SL(2, Z) with spectral parameter tj. We prove, for the first time, some hybrid subconvexity bounds for the twisted L-functions on GL(3), such as L(1/2, Φ× uj ×χ) ■Φ,ε(q(1 + |tj |))3/2-θ+ε and L(1/2 + it, Φ×χ) ■Φ,ε(q(1 + |t|))3/4-θ/2+ε for any ε > 0, where θ = 1/23 is admissible. The proofs depend on the first moment of a family of L-functions in short intervals. In order to bound this moment, we first use the approximate functional equations, the Kuznetsov formula, and the Voronoi formula to transform it to a complicated summation, and then we apply different methods to estimate it, which give us strong bounds in different aspects. We also use the stationary phase method and the large sieve inequalities.

关 键 词：L-FUNCTIONS subconvexity GL(3) TWISTED quadratic character 

分 类 号：O156.4[理学—数学]