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- W2963444837 abstract "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 Г0(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 $$Lleft( {1/2,phi times {u_j} times chi } right){ ll _{phi ,varepsilon }}{left( {qleft( {1 + left| {{t_j}} right|} right)} right)^{3/2 - theta + varepsilon }},Lleft( {1/2 + it,phi times chi } right){ ll _{phi ,varepsilon }}{left( {qleft( {1 + left| t right|} right)} right)^{3/4 - theta /2 + varepsilon }},$$ 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." @default.
- W2963444837 created "2019-07-30" @default.
- W2963444837 creator A5004908848 @default.
- W2963444837 date "2019-04-25" @default.
- W2963444837 modified "2023-10-02" @default.
- W2963444837 title "Hybrid subconvexity bounds for twisted L-functions on GL(3)" @default.
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- W2963444837 doi "https://doi.org/10.1007/s11425-017-9428-6" @default.
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