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L-FUNCTION: 作品数：38被引量：21H指数：3; 导出分析报告; 相关领域：理学更多>>; 相关作者：王鑫更多>>; 相关机构：山东大学更多>>; 相关期刊：《Science China Chemistry》《Science China Mathematics》《Acta Mathematica Scientia》《Chinese Annals of Mathematics,Series B》更多>>; 相关基金：国家自然科学基金国家重点基础研究发展计划中国科学院科研项目中国博士后科学基金更多>>

On the Higher Moments of Coefficients Attached to Dedekind Zeta Function: 《数学进展》2024年第6期1188-1198,共11页HUA Guodong; Supported in part by NSFC (Nos.12401011,12201214);National Key Research and Development Program of China (No.2021YFA1000700);Natural Science Basic Research Program of Shaanxi (Nos.2023-JC-QN-0024,2023-JC-YB-077);Foundation of Shaanxi Educational Committee (No.2023-JCYB-013);Shaanxi Fundamental Science Research Project for Mathematics and Physics (Nos.23JSQ053,22JSQ010);Scientific Research Foundation of WNU。; Let K_(3) be a non-normal cubic extension over Q.In this paper,we investigate the higher moments of the coefficients a_(K_(3))(n) of Dedekind zeta function over sum of two squares of the following types■ where l≥9 i...; 关键词：non-normal cubic field Dedekind zeta function Rankin-Selberg L-function

Omega results for coefficients of Rankin-Selberg L-functions over sparse sequences: 《纯粹数学与应用数学》2024年第3期407-416,共10页CUI Hanfang LAO Huixue; 国家自然科学基金(12201363).; Ω results involving the coefficients of automorphic L-functions are important research object in analytic number theory.Let f be a primitive holomorphic cusp form.Denote by λ_(f×f)(n) the nth Fourier coefficient of...; 关键词：cusp form Rankin-Selberg L-function Omega theorem

Lower Bounds for Moments of Quadratic Twisted Self-dual GL(3)Central L-values: 《Acta Mathematica Sinica,English Series》2023年第11期2139-2148,共10页Sheng Hao HUA Bing Rong HUANG; National Key R&D Program of China(Grant No.2021YFA1000700);NSFC(Grant Nos.12001314 and 12031008)。; In this paper,we prove the conjectured order lower bound for the k-th moment of central values of quadratic twisted self-dual GL(3)L-functions for all k≥1,based on our recent work on the twisted first moment of centr...; 关键词：GL(3)cusp form lower bound quadratic twist central value L-FUNCTION

Rankin-Selberg convolutions for GL(n)×GL(n)and GL(n)×GL(n-1)for principal series representations: 《Science China Mathematics》2023年第10期2203-2218,共16页Jian-Shu Li Dongwen Liu Feng Su Binyong Sun; supported by the Natural Science Foundation of Zhejiang Province(Grant No.LZ22A010006);National Natural Science Foundation of China(Grant No.12171421);Feng Su was supported by National Natural Science Foundation of China(Grant No.11901466);the Qinglan Project of Jiangsu Province;supported by the National Key Research and Development Program of China(Grant No.2020YFA0712600).; Let k be a local field.Let I_(v) and I_(v′)be smooth principal series representations of GLn(k)and GL_(n-1)(k),respectively.The Rankin-Selberg integrals yield a continuous bilinear map I_(v)×I_(v′)→C with a certai...; 关键词：principal series representation Rankin-Selberg convolution L-FUNCTION

GENERIC NEWTON POLYGON OF THE L-FUNCTION OF n VARIABLES OF THE LAURENT POLYNOMIAL I: 《Acta Mathematica Scientia》2022年第6期2419-2436,共18页Fusheng LENG; The Hodge bound for the Newton polygon of L-functions of T-adic exponential sums associated to a Laurent polynomial is established.We improve the lower bound and study the properties of this new bound.We also study wh...; 关键词：exponential sum Hodge bound combinatorial Newton polygon

Double square moments and subconvexity bounds for Rankin-Selberg L-functions of holomorphic cusp forms: 《Science China Mathematics》2020年第5期823-844,共22页Jianya Liu Haiwei Sun Yangbo Ye; supported by National Natural Science Foundation of China(Grant No.11531008);Ministry of Education of China(Grant No.IRT16R43);Taishan Scholar Project of Shandong Province;supported by National Natural Science Foundation of China(Grant No.11601271);China Postdoctoral Science Foundation(Grant No.2016M602125);China Scholarship Council(Grant No.201706225004)。; 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...; 关键词：automorphic L-function congruence subgroup cusp form holomorphic cusp form Rankin-Selberg L-function square moment subconvexity bound

Mean-square estimate of automorphic L-functions: 《Frontiers of Mathematics in China》2020年第1期205-213,共9页Weili YAO; the National Natural Science Foundation of China(Grant No.11601309).; Let f be a holomorphic Hecke cusp form with even integral weight k≥2 for the full modular group,and letχbe a primitive Dirichlet character modulo q.Let Lf(s,χ)be the automorphic L-function attached to f andχ-We st...; 关键词：Automorphic L-FUNCTION CUSP FORM FOURIER COEFFICIENT

Several Expressions of Dirichlet L-function at Positive Integers: 《Acta Mathematica Sinica,English Series》2019年第9期1549-1562,共14页Yuan HE; Supported by the National Natural Science Foundation of China(Grant No.11326050); In this paper, by making use of Abel’s theorem on power series, the reflection formula and the function equation for Hurwitz zeta function, we establish several expressions of Dirichlet Lfunction at positive integers...; 关键词：DIRICHLET L-FUNCTION trigonometric SUMS GAUSS SUMS BERNOULLI polynomials combinatorial IDENTITIES

Basic functions and unramified local L-factors for split groups被引量：1: 《Science China Mathematics》2017年第5期777-812,共36页LI Wen-Wei; According to a program of Braverman, Kazhdan and NgS, for a large class of split unramified reductive groups G and representations p of the dual group G, the unramified local L-factor L（s, π, ρ） can be expressed a...; 关键词：L-FUNCTION Satake isomorphism generalized Kostka-Foulkes polynomial

A critical case of Rallis inner product formula: 《Science China Mathematics》2017年第2期201-222,共22页WU ChenYan; Letπbe a genuine cuspidal representation of the metaplectic group of rank n.We consider the theta lifts to the orthogonal group associated to a quadratic space of dimension 2n+1.We show a case of regularised Rallis i...; 关键词：regularised Siegel-Weil formula Rallis inner product formula theta lift L-FUNCTION

L-FUNCTION