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, fo...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.展开更多
Let f and g be holomorphic cusp forms of weights k1 and k2 for the congruence subgroups TO(N1)and Γ0(N2),respectively.In this paper the square moment of the Rankin-Selberg L-function for f and g in the aspect of both...Let f and g be holomorphic cusp forms of weights k1 and k2 for the congruence subgroups TO(N1)and Γ0(N2),respectively.In this paper the square moment of the Rankin-Selberg L-function for f and g in the aspect of both weights in short intervals is bounded,when k1^ε <<k^2<<k1^1-ε.These bounds are the mean Lindelof hypothesis in one case and subconvexity bounds on average in other cases.These square moment estimates also imply subconvexity bounds for individual L(1/2+it,f×g) for all g when f is chosen outside a small exceptional set.In the best case scenario the subconvexity bound obtained reaches the Weyl-type bound proved by Lau et al.(2006) in both the k1 and k2 aspects.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11531008)the Ministry of Education of China(Grant No.IRT 16R43)。
文摘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.
基金supported by National Natural Science Foundation of China(Grant No.11531008)Ministry of Education of China(Grant No.IRT16R43)+3 种基金Taishan Scholar Project of Shandong Provincesupported by National Natural Science Foundation of China(Grant No.11601271)China Postdoctoral Science Foundation(Grant No.2016M602125)China Scholarship Council(Grant No.201706225004)。
文摘Let f and g be holomorphic cusp forms of weights k1 and k2 for the congruence subgroups TO(N1)and Γ0(N2),respectively.In this paper the square moment of the Rankin-Selberg L-function for f and g in the aspect of both weights in short intervals is bounded,when k1^ε <<k^2<<k1^1-ε.These bounds are the mean Lindelof hypothesis in one case and subconvexity bounds on average in other cases.These square moment estimates also imply subconvexity bounds for individual L(1/2+it,f×g) for all g when f is chosen outside a small exceptional set.In the best case scenario the subconvexity bound obtained reaches the Weyl-type bound proved by Lau et al.(2006) in both the k1 and k2 aspects.
