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Poles of l-functions on Quaternion Groups

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Chinese Annals of Mathematics,Series B 2014年第4期35卷 519-526页

作者： ?etin üRTS Department of Mathematics TOBB University of Economics and Technology Ankara Turkey

The author shows that the(partial) standard langlands l-functions on quarternion groups have at most simple poles at certain positive integers.

关键词： Siegel Eisenstein series l-functions Quaternion groups RegularizedSiegel-Weil formula

The First Power Mean of the Inversion of l-functions Weighted by Quadratic Gauss Sums

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Acta Mathematica Sinica,English Series 2004年第2期20卷 283-292页

作者： WenPengZHANG ResearchCenterforBasicScience Xi'anJiaotongUniversityXi'an710049P.R.China

The main purpose of this paper is to use estimates for character sums and analytic methods to study the first power mean of the inversion of Dirichlet l-functions with the weight of general quadratic Gauss sums,and th... 详细信息

关键词： General quadratic Gauss sums l-functions Asymptotic formula

A New Zero-density Result of l-functions Attached to Maass Forms

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Acta Mathematica Sinica,English Series 2011年第6期27卷 1149-1162页

作者： Zhao XU School of Mathematics Shandong University Ji'nan 250100 P. R. China

let f denote a normalized Maass cusp form for Sl（2, Z）, which is an eigenfunction of all the Hecke operators T（n） as well as the reflection operator T-1： z →z. We obtain a zero-density result of the l-function a... 详细信息

关键词： Zero-density automorphic forms l-functions

Periods of automorphic forms,poles of l-functions and functorial lifting

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Science China Mathematics 2010年第9期53卷 2215-2238页

作者： GINZBURG David SOUDRY David School of Mathematical Sciences Sackler Faculty of Exact SciencesTel-Aviv University69978Israel

In this paper,we survey our work on period,poles or special values of certain automorphic lfunctions and their relations to certain types of langlands functorial *** outline proofs for some results and leave others as... 详细信息

关键词： period of automorphic forms l-functions langlands functoriality

Zero-free Regions for Dirichlet l-functions and the Exceptional Set of Goldbach Numbers

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数学进展 1997年第6期26卷 82-83页

作者：李红泽山东大学数学系山东济南

Ｚｅｒｏ－ｆｒｅｅＲｅｇｉｏｎｓｆｏｒＤｉｒｉｃｈｌｅｔＬ－ｆｕｎｃｔｉｏｎｓａｎｄｔｈｅＥｘｃｅｐｔｉｏｎａｌＳｅｔｏｆＧｏｌｄｂａｃｈＮｕｍｂｅｒｓＬｉＨｏｎｇｚｅ（李红泽）ＭＲ（１９９１）ＳｕｂｊｅｃｔＣｌａｓ... 详细信息

Ｚｅｒｏ－ｆｒｅｅＲｅｇｉｏｎｓｆｏｒＤｉｒｉｃｈｌｅｔＬ－ｆｕｎｃｔｉｏｎｓａｎｄｔｈｅＥｘｃｅｐｔｉｏｎａｌＳｅｔｏｆＧｏｌｄｂａｃｈＮｕｍｂｅｒｓＬｉＨｏｎｇｚｅ（李红泽）ＭＲ（１９９１）ＳｕｂｊｅｃｔＣｌａｓｉｆｉｃａｔｉｏｎ：１１Ｎ１３，１...

关键词：李红 l-functions and the Set Regions Exceptional Dirichlet

Sums of Five Almost Equal Prime Squares

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Acta Mathematica Sinica,English Series 2005年第4期21卷 833-840页

作者： Claus BAUER Dolby laboratories 100 Potrero AvenueSan FranciscoCA94103USA

let Pi, 1≤i≤5, be prime numbers. It is proved that every integer N that satisfies N=5 （mod 24） can be written as N=p1^2＋p2^2＋P3^2＋p4^2 ＋p5^2, where │√N5-Pi│≤N^1/2-19/850＋∈.

关键词： Prime numbers Exponential sums l-functions

Exponential Sums over Finite Fields

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Journal of Systems Science & Complexity 2021年第4期34卷 1225-1278页

作者： WAN Daqing Department of Mathematics University of CaliforniaIrvineCA 92697-3875USA

This is an expository paper on algebraic aspects of exponential sums over finite *** is a new *** examples,results and open problems are presented along the way,with particular emphasis on Gauss periods,Kloosterman sums and one variable exponential *** main tool is the applications of various p-adic *** this reason,the author has also included a brief exposition of certain p-adic estimates of exponential *** material is based on the lectures given at the 2020 online number theory summer school held at Xiamen *** were taken by Shaoshi Chen and Ruichen Xu.

关键词： Degrees of exponential sums finite fields Gauss sums Kloosterman sums l-functions

AlGEBRAIC DIFFERENTIAl INDEPENDENCE CONCERNING THE EUlER Γ-FUNCTION AND DIRICHlET SERIES

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Acta Mathematica Scientia 2020年第4期40卷 1035-1044页

作者： Wei CHEN Qiong WANG School of Sciences Chongqing University of Posts and TelecommunicationsChongqing 400065China

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, or some periodic functions. We prove that the EulerΓ-function and the function F cannot satisfy any nontrivial algebraic differential equations whose coefficients are meromorphic functions Ø with ρ(Ø) < 1.

关键词： Gamma function l-functions algebraic differential independence algebraic differential equations

Generalization of Bombieri's theorem and its applications

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Science China Mathematics 1995年第12期38卷 1432-1443页

作者：林家发展涛 Department of Mathematics Shandong University Jinan 250100 China

By using the so-called Hooley-Huxley Contour and zero density estimates for Dirichlet l-function, Bombieri’s theorem is established for a class of arithmetic functions whose generating functions satisfy certain analytic conditions. As applications of our theorem, the mean value estimates of l-functions and the distribution of integers representable as sums of two squares are discussed.

关键词： Bombieri’ s theorem Dirichlet l-functions mean value estimates.