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Locally and globally uniform approximations for ruin probabilities of a nonstandard bidimensional risk model with subexponential claims

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Applied Mathematics(A Journal of Chinese Universities) 2024年第1期39卷 98-113页

作者： LIU Zai-ming GENG Bing-zhen WANG Shi-jie School of Mathematics and Statistics Central South UniversityChangsha 410083China School of Big Data and Statistics Anhui UniversityHefei 230601China

Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily *** some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite *** we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.

关键词： bidimensional risk model asymptotic formula subexponential distribution consistently varying tail ruin probability

Powers of General Digital Sums

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Acta Mathematica Sinica,English Series 2010年第6期26卷 1133-1138页

作者： Feng Juan CHEN School of Mathematical Sciences Nanjing Normal University Nanjing 210046 P. R. China and Department of Mathematics Suzhou University Suzhou 215006 P. R. China

Let m0,m1,m2,…be positive integers with mi〉 2 for all i. It is well known that each nonnegative integer n can be uniquely represented as n= a0 ＋ a1m0＋a2m0m1＋…＋atm0m1m2…mt-1,where 0≤ai≤mi-1 for all i and at≠*** each fi be a function defined on {0,1,2…,mi-1} with fi（0）=*** S（n）=i=0∑tfi（ai）.In this paper, we give the asymptotic formula for x^-1∑n≤xS（n）^k,where k is a positive integer.

关键词： digital sum arithmetic function asymptotic formula

On the Number of Integral Ideals in Two Different Quadratic Number Fields

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Chinese Annals of Mathematics,Series B 2016年第4期37卷 595-606页

作者： Zhishan YANG School of Mathematics and Statistics Northeast Normal University

Let K be an algebraic number field of finite degree over the rational field ~, and aK （n） the number of integral ideals in K with norm n. When K is a Galois extension over Q, many authors contribute to the integral power sums of aK（n）,This paper is interested in the distribution of integral ideals concerning different number fields. The author is able to establish asymptotic formulae for the convolution sumwhere K1 and K2 are two different quadratic fields.

关键词： asymptotic formula Integral ideal Number field 17B40 17B50

On the 2k-th Power Mean of Inversion of L-functions with the Weight of the Gauss Sum

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Acta Mathematica Sinica,English Series 2004年第1期20卷 175-180页

作者： YuanYI WenPengZHANG ResearchCenterforBasicScience Xi'anJiaotongUniversityXi'an710067P.R.China ResearchCenterforBasicScience Xi'anJiaotongUniversityXi'an710067P.R.China

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, ... 详细信息

关键词： Dirichlet L-functions Gauss sums Mean value asymptotic formula

On the Mean Value formula of Dedekind Sums

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Acta Mathematica Sinica,English Series 1999年第2期15卷 245-254页

作者： Xiali He Wenpeng Zhang, Department of Mathematics, Northwest University, Xi’an 710069, P. R. China Department of Mathematics Northwest University Xi’an P. R. China

The main purpose of this paper is to use the mean value theorem of the Dirichlet L-function to study the distribution property of Dedekind sums, and to give a sharper mean value formula.

关键词： Dedekind sums Distribution of the mean value asymptotic formula

On the Character Sum of Polynomials and the Two-term Exponential Sums

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Acta Mathematica Sinica,English Series 2020年第2期36卷 196-206页

作者： Xing Xing LV Wen Peng ZHANG School of Mathematics Northwest University

The main purpose of this paper is using the analytic method and the properties of the character sums to study the computational problem of one kind hybrid power mean involving the character sums of polynomials and the... 详细信息

关键词： Character sums of polynomials two-term exponential sums hybrid power mean analytic method asymptotic formula

On the Fourth Power Mean of the Character Sums Over Short Intervals

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Acta Mathematica Sinica,English Series 2007年第1期23卷 153-164页

作者： Wen Peng ZHANG Xiao Ying WANG Research Center for Basic Science Xi'an Jiaotong University Xi'an 710049 P. R. China

The main purpose of this paper is to study the mean value properties of the character sums over the interval [1,p/8） by using the mean value theorems of the Dirichlet L-functions, and give an interesting mean value f... 详细信息

关键词： character sums short intervals fourth power mean asymptotic formula

On the Fourth Power Moment of Fourier Coefficients of Cusp Form

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Acta Mathematica Sinica,English Series 2018年第6期34卷 1050-1058页

作者： Jin Jiang LI Pan Wang WANG Min ZHANG Department of Mathematics China University of Mining and Technology

Let a（n） be the Fourier coefficients of a holomorphic cusp form of weight κ = 2n ≥ 12 for the full modular group and A（x） =∑n≤xa（n）.In this paper, we establish an asymptotic formula of tile fourth power moment of A（x） and prove that ∫1^TA^4（x）dx=3/64κπ^4s4;2（a^~）T^2κ＋O（T^2a-δ4＋t） with δ4 = 1/8, which improves the previous result.

关键词： Cusp form Fourier coefficient mean value asymptotic formula

Manin’s conjecture for a class of singular cubic hypersurfaces

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Frontiers of Mathematics in China 2022年第6期17卷 1089-1132页

作者： Wenguang ZHAI Department of Mathematics China University of Mining and TechnologyBeijing100083China

Letℓ≥2 be a fixed positive integer and Q(y)be a positive definite quadratic form inℓvariables with integral *** aim of this paper is to count rational points of bounded height on the cubic hypersurface defined by u^(... 详细信息

关键词： Manin’s conjecture quadratic form asymptotic formula divisor problem exponential sum