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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

A supplement to Chebotarev's density theorem被引量：1: 《Science China Mathematics》2023年第12期2749-2753,共5页Gergely Harcos Kannan Soundararajan; supported by the Rényi Intézet Lendület Automorphic Research Group and NKFIH(National Research,Development and Innovation Office)(Grant No.K 143876);supported in part by a grant from the National Science Foundation;a Simons Investigator Award from the Simons Foundation。; Let L/K be a Galois extension of number fields with Galois group G.We show that if the density of prime ideals in K that split totally in L tends to 1/|G|with a power saving error term,then the density of prime ideals...; 关键词：Chebotarev's density theorem Artin L-functions Heilbronn characters

Rankin-Selberg coefficients in large arithmetic progressions被引量：1: 《Science China Mathematics》2023年第12期2767-2778,共12页Emmanuel Kowalski Yongxiao Lin Philippe Michel; supported by the SNF(Grant No.200021_197045)。; Let(λ_f(n))_(n≥1)be the Hecke eigenvalues of either a holomorphic Hecke eigencuspform or a Hecke-Maass cusp form f.We prove that,for any fixedη>0,under the Ramanujan-Petersson conjecture for GL_(2)Maass forms,the R...; 关键词：arithmetic progressions Rankin-Selberg L-functions δ-method

Exponential Sums over Finite Fields被引量：2: 《Journal of Systems Science & Complexity》2021年第4期1225-1278,共54页WAN Daqing; partially supported by the National Natural Science of Foundation under Grant No.1900929。; This is an expository paper on algebraic aspects of exponential sums over finite fields.This is a new direction.Various examples,results and open problems are presented along the way,with particular emphasis on Gauss ...; 关键词：Degrees of exponential sums finite fields Gauss sums Kloosterman sums L-FUNCTIONS

Hybrid subconvexity bounds for twisted L-functions on GL(3)被引量：1: 《Science China Mathematics》2021年第3期443-478,共36页Bingrong Huang; supported by National Natural Science Foundation of China(Grant No.11531008);the Ministry of Education of China(Grant No.IRT 16R43)。; 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...; 关键词：L-FUNCTIONS subconvexity GL(3) TWISTED quadratic character

The second moment of GL(3)×GL(2)L-functions at special points from GL(3)forms: 《Frontiers of Mathematics in China》2020年第5期1071-1088,共18页Zhao XU; supported by the Natural Science Foundation of Shandong Province[ZR2019MA011];Young Scholars Program of Shandong University[2017WLJH12].; For a fixed even SL(2,Z)Hecke-Maass form f,we get an estimate for the second moment of L(s,φj×f)at special points,whereφj runs over an orthogonal basis of Hecke-Maass cusp forms for SL3(Z).; 关键词：Rankin-Selberg L-functions Hecke-Maass forms Kuznetsov trace formula

ALGEBRAIC DIFFERENTIAL INDEPENDENCE CONCERNING THE EULER Γ-FUNCTION AND DIRICHLET SERIES: 《Acta Mathematica Scientia》2020年第4期1035-1044,共10页Wei CHEN Qiong WANG; by Basic and Advanced Research Project of CQCSTC(cstc2019jcyj-msxmX0107);Fundamental Research Funds of Chongqing University of Posts and Telecommunications(CQUPT:A2018-125).; This article investigates the algebraic differential independence concerning the Euler Γ-function and the function F in a certain class F which contains Dirichlet L-functions,L-functions in the extended Selberg class...; 关键词：Gamma function L-FUNCTIONS algebraic differential independence algebraic differential equations

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

The Riemann Hypothesis and Emergent Phase Space: 《Journal of Modern Physics》2017年第4期459-482,共24页Daniel Brox; By interpreting multifractal L-function zero alignment as a decoherence process, the Riemann hypothesis is demonstrated to imply the emergence of classical phase space at zero alignment. This provides a conception of ...; 关键词：RIEMANN HYPOTHESIS Emergent Phase Space L-FUNCTIONS MODULAR FORMS

Oscillations of coefficients of symmetric square L-functions over primes: 《Frontiers of Mathematics in China》2015年第6期1325-1341,共17页Fei HOU; Let L（s, sym2f） be the symmetric-square L-function associated to a primitive holomorphic cusp form f for SL（2, Z）, with tf（n, 1） denoting the nthcoefficient of the Dirichlet series for it. It is proved that, for...; 关键词：symmetric-square L-function primitive holomorphic cusp form Fourier coefficient

L-FUNCTIONS