In this paper,we use the elementary methods,the properties of Dirichlet character sums and the classical Gauss sums to study the estimation of the mean value of high-powers for a special character sum modulo a prime,a...In this paper,we use the elementary methods,the properties of Dirichlet character sums and the classical Gauss sums to study the estimation of the mean value of high-powers for a special character sum modulo a prime,and derive an exact computational formula.It can be conveniently programmed by the“Mathematica”software,by which we can get the exact results easily.展开更多
The main purpose of this paper is, using the analytic method, to study the mean value properties of the complete trigonometric sums with Dirichlet characters, and give an exact calculating formula for its fourth power...The main purpose of this paper is, using the analytic method, to study the mean value properties of the complete trigonometric sums with Dirichlet characters, and give an exact calculating formula for its fourth power mean.展开更多
A sharper asymptotic formula for the mean value sum from xmodq*L′(σ+it,X)L′(1-σ-it,X)1(where the summation is over all primitive Dirichlet characters mod q and 0<σ<1) is derived by using the analytic method...A sharper asymptotic formula for the mean value sum from xmodq*L′(σ+it,X)L′(1-σ-it,X)1(where the summation is over all primitive Dirichlet characters mod q and 0<σ<1) is derived by using the analytic method and the estimate of character sums.展开更多
The main purpose of this paper is using residue system and character sums methods to investigate the mean value properties of general k-th Gauss sums,and two exact calculating formulas are given.
Ⅰ. INTRODUCTIONFor an integer q≥3, let X denote a typical Dirichlet character modulo q, and L(s, X) be the corresponding Dirichlet L-function. [1] studied the asymptotic property of mean value sum from X_q≠X_q^0 |L...Ⅰ. INTRODUCTIONFor an integer q≥3, let X denote a typical Dirichlet character modulo q, and L(s, X) be the corresponding Dirichlet L-function. [1] studied the asymptotic property of mean value sum from X_q≠X_q^0 |L(1, X)|~4, and showed the following asymptotic formula:展开更多
Let p≥5 be a prime. For any integer h, the Hardy sum is defined by H(h,p)=sum((-1)^(j+1+[(hj)/p]))from (p-1) to (j=1) which is related to the classical Dedekind sum. The mean values of the Hardy sum in short interval...Let p≥5 be a prime. For any integer h, the Hardy sum is defined by H(h,p)=sum((-1)^(j+1+[(hj)/p]))from (p-1) to (j=1) which is related to the classical Dedekind sum. The mean values of the Hardy sum in short intervals are studied by using the mean value theorems of Dirichlet L-functions.展开更多
I. INTRODUCTIONFor an integer q】2, 1et x denote a typical Dirichlet character mod q, x<sub>0</sub> the principal character, and L（s, x） the corresponding Dirichlet L-function. The main purpose of this n...I. INTRODUCTIONFor an integer q】2, 1et x denote a typical Dirichlet character mod q, x<sub>0</sub> the principal character, and L（s, x） the corresponding Dirichlet L-function. The main purpose of this note is to give a more accurate asymptotic formula for the fourth power展开更多
The main purpose of this paper is to use the estimate for character sums and the method of trigonometric sums to study the 2k-th power mean of the inversion of Dirichlet L-functions with the weight of the Gauss sums, ...The main purpose of this paper is to use the estimate for character sums and the method of trigonometric sums to study the 2k-th power mean of the inversion of Dirichlet L-functions with the weight of the Gauss sums, and give a sharper asymptotic formula.展开更多
对正整数K和任意整数H,DEDEKIND和定义为:S(H,K)=SUM FORM A=1 TO K((A/K))((AH/K)),其中 (H,K)=1 且利用DIRICHLET L-函数的均值定理研究了DEDEKIND和与原特征Χ*的混合均值SUM FROM H=1 TO K Χ*(H) |S(H,K)|2,并给出了一个有趣的渐...对正整数K和任意整数H,DEDEKIND和定义为:S(H,K)=SUM FORM A=1 TO K((A/K))((AH/K)),其中 (H,K)=1 且利用DIRICHLET L-函数的均值定理研究了DEDEKIND和与原特征Χ*的混合均值SUM FROM H=1 TO K Χ*(H) |S(H,K)|2,并给出了一个有趣的渐近公式．展开更多
文摘In this paper,we use the elementary methods,the properties of Dirichlet character sums and the classical Gauss sums to study the estimation of the mean value of high-powers for a special character sum modulo a prime,and derive an exact computational formula.It can be conveniently programmed by the“Mathematica”software,by which we can get the exact results easily.
文摘The main purpose of this paper is, using the analytic method, to study the mean value properties of the complete trigonometric sums with Dirichlet characters, and give an exact calculating formula for its fourth power mean.
基金Project supported by the National Natural Science Foundation of China.
文摘A sharper asymptotic formula for the mean value sum from xmodq*L′(σ+it,X)L′(1-σ-it,X)1(where the summation is over all primitive Dirichlet characters mod q and 0<σ<1) is derived by using the analytic method and the estimate of character sums.
基金Supported by the National Natural Science Foundation of China (Grant No.11071194)the Northwest University Doctorate Dissertation of Excellence Funds (Grant No.09YYB05)
文摘The main purpose of this paper is using residue system and character sums methods to investigate the mean value properties of general k-th Gauss sums,and two exact calculating formulas are given.
文摘Ⅰ. INTRODUCTIONFor an integer q≥3, let X denote a typical Dirichlet character modulo q, and L(s, X) be the corresponding Dirichlet L-function. [1] studied the asymptotic property of mean value sum from X_q≠X_q^0 |L(1, X)|~4, and showed the following asymptotic formula:
基金Supported by the National Natural Science Foundation of China(11571277)Supported by the Science and Technology Program of Shaanxi Province(2016GY-077)
文摘Let p≥5 be a prime. For any integer h, the Hardy sum is defined by H(h,p)=sum((-1)^(j+1+[(hj)/p]))from (p-1) to (j=1) which is related to the classical Dedekind sum. The mean values of the Hardy sum in short intervals are studied by using the mean value theorems of Dirichlet L-functions.
文摘I. INTRODUCTIONFor an integer q】2, 1et x denote a typical Dirichlet character mod q, x<sub>0</sub> the principal character, and L（s, x） the corresponding Dirichlet L-function. The main purpose of this note is to give a more accurate asymptotic formula for the fourth power
基金supported by the Doctorate Foundation of Xi'an Jiaotong University
文摘The main purpose of this paper is to use the estimate for character sums and the method of trigonometric sums to study the 2k-th power mean of the inversion of Dirichlet L-functions with the weight of the Gauss sums, and give a sharper asymptotic formula.
文摘对正整数K和任意整数H,DEDEKIND和定义为:S(H,K)=SUM FORM A=1 TO K((A/K))((AH/K)),其中 (H,K)=1 且利用DIRICHLET L-函数的均值定理研究了DEDEKIND和与原特征Χ*的混合均值SUM FROM H=1 TO K Χ*(H) |S(H,K)|2,并给出了一个有趣的渐近公式．
