In this paper, we establish asymptotic formulas for a cubic moment of Dirichlet L-functions restricted to a coset, as well as for a mixed moment of Dirichlet L-functions and twists of GL(2) L-functions along a coset. ...In this paper, we establish asymptotic formulas for a cubic moment of Dirichlet L-functions restricted to a coset, as well as for a mixed moment of Dirichlet L-functions and twists of GL(2) L-functions along a coset. Our main tool is a power-saving estimate of bilinear forms of hyper-Kloosterman sums due to Kowalski–Michel–Sawin.展开更多
In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a se...In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet L-functions. This study is a generalization of Akatsuka’s theorem on the Riemann zeta function, and gives a proof of Kurokawa’s prediction proposed in 1992.展开更多
Let q ≥ 3 be an integer, and χ be a Dirichlet character modulo q, L（s, χ） denote the Dirichlet L-function corresponding to χ. In this paper, we show some early information on the mean value of the Dirichlet L-fu...Let q ≥ 3 be an integer, and χ be a Dirichlet character modulo q, L（s, χ） denote the Dirichlet L-function corresponding to χ. In this paper, we show some early information on the mean value of the Dirichlet L-functions and give some new identities forwhere a = 2, 3, or 4. Then we give general identities for the case that the integer a divides q - 1. Keywords Dirichlet L-functions, Dedekind sum, trigonometric formula, MSbius inversion formula展开更多
基于弹着点空间分布对目标毁伤效能的差异化影响,构建导弹命中目标不同重要区域的概率分布模型,实现对传统命中精度概念的扩展。针对导弹实打试验过程复杂、费用高、次数少的实际,采用贝叶斯方法融合多源信息,基于区域划分-分布确定-先...基于弹着点空间分布对目标毁伤效能的差异化影响,构建导弹命中目标不同重要区域的概率分布模型,实现对传统命中精度概念的扩展。针对导弹实打试验过程复杂、费用高、次数少的实际,采用贝叶斯方法融合多源信息,基于区域划分-分布确定-先验融合-后验求解的思路进行导弹命中精度估计。选取Dirichlet分布作为命中精度参数的先验分布,运用D-S(Dempster-Shafer)证据理论对先验信息进行融合处理,基于马尔可夫链蒙特卡罗(Markov chain Monte Carlo, MCMC)方法对精度参数的后验分布进行求解。示例表明,该方法能够细致描述导弹命中目标不同重要区域的概率,并科学融合多源命中精度先验信息,为导弹命中精度估计方法及测试方案优化提供理论借鉴。展开更多
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...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 by means of some finite sums of different types. Some special cases as well as immediate consequences of the results presented here are also considered.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
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
For integer q≥3, let X denote a typical Dirichlet character mod q, and L(s, X)be the corresponding Dirichlet L-function. We define the function A(q, k)and B(q, k)as follows:
Letλ_(f×f)(n)be the nth Fourier coeficient of Rankin-Selberg L-function L(f×f,s).In this paper,we are interested in the average behavior of coeficients of Rankin-Selberg L-functions over sparse sequences,an...Letλ_(f×f)(n)be the nth Fourier coeficient of Rankin-Selberg L-function L(f×f,s).In this paper,we are interested in the average behavior of coeficients of Rankin-Selberg L-functions over sparse sequences,and establish the asymptotic formula ofΣ_(n≤xλ_(f×f)n^(m)).展开更多
In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditio...In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.展开更多
基金Supported by the National Key R&D Program of China(Grant No.2021YFA1000700)National Natural Science Foundation of China(Grant No.12031008)。
文摘In this paper, we establish asymptotic formulas for a cubic moment of Dirichlet L-functions restricted to a coset, as well as for a mixed moment of Dirichlet L-functions and twists of GL(2) L-functions along a coset. Our main tool is a power-saving estimate of bilinear forms of hyper-Kloosterman sums due to Kowalski–Michel–Sawin.
文摘In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet L-functions. This study is a generalization of Akatsuka’s theorem on the Riemann zeta function, and gives a proof of Kurokawa’s prediction proposed in 1992.
基金Supported by Basic Research Fund of the Northwestern Polytechnical University of China(Grant Nos.JC2011023 and JC2012252)
文摘Let q ≥ 3 be an integer, and χ be a Dirichlet character modulo q, L（s, χ） denote the Dirichlet L-function corresponding to χ. In this paper, we show some early information on the mean value of the Dirichlet L-functions and give some new identities forwhere a = 2, 3, or 4. Then we give general identities for the case that the integer a divides q - 1. Keywords Dirichlet L-functions, Dedekind sum, trigonometric formula, MSbius inversion formula
文摘基于弹着点空间分布对目标毁伤效能的差异化影响,构建导弹命中目标不同重要区域的概率分布模型,实现对传统命中精度概念的扩展。针对导弹实打试验过程复杂、费用高、次数少的实际,采用贝叶斯方法融合多源信息,基于区域划分-分布确定-先验融合-后验求解的思路进行导弹命中精度估计。选取Dirichlet分布作为命中精度参数的先验分布,运用D-S(Dempster-Shafer)证据理论对先验信息进行融合处理,基于马尔可夫链蒙特卡罗(Markov chain Monte Carlo, MCMC)方法对精度参数的后验分布进行求解。示例表明,该方法能够细致描述导弹命中目标不同重要区域的概率,并科学融合多源命中精度先验信息,为导弹命中精度估计方法及测试方案优化提供理论借鉴。
基金Supported by the National Natural Science Foundation of China(Grant No.11326050)
文摘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 by means of some finite sums of different types. Some special cases as well as immediate consequences of the results presented here are also considered.
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.
文摘For integer q≥3, let X denote a typical Dirichlet character mod q, and L(s, X)be the corresponding Dirichlet L-function. We define the function A(q, k)and B(q, k)as follows:
基金Supported by Natural Science Foundation of Shandong Province(No.ZR2024MA053)。
文摘Letλ_(f×f)(n)be the nth Fourier coeficient of Rankin-Selberg L-function L(f×f,s).In this paper,we are interested in the average behavior of coeficients of Rankin-Selberg L-functions over sparse sequences,and establish the asymptotic formula ofΣ_(n≤xλ_(f×f)n^(m)).
基金supported by the National Natural Science Foundation of China(12171373)Chen's work also supported by the Fundamental Research Funds for the Central Universities of China(GK202207018).
文摘In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.
