On the Mean Square Formula of the Error Termfor a Class of Arithmetical Functions

 Based on the method in Meurman [5], we study the mean square formula of the error term for a class of Arithmetical functions whose Dirichlet series satisfies a functional equation with multiple gamma factors. We obtain improvements on some results of Chandrasekharan and Narasimhan [1]. (Received 29 June 1998; in final form 11 November 1998)     

关于L—函数的二次均值公式

本文利用三角和估值的指数偶方法,改进了张文鹏关于Dirichlet L—函数的二次均值(?)│L(1/2+it,x)│²的一个渐近公式.     

Summatory Formula of the Convolution of Two Arithmetical Functions

 We study the asymptotic formula of for some arithmetical functions f and g. This generalizes the case investigated by Balakrishnan and Pétermann.     

Summatory Formula of the Convolution of Two Arithmetical Functions

 We study the asymptotic formula of for some arithmetical functions f and g. This generalizes the case investigated by Balakrishnan and Pétermann. Received 15 January 2001; in revised form 7 July 2001     

一些新的数论函数及其均值公式

对于给定的自然数m,我们利用最大公约数和最小公倍数定义数论函数(m,n)和[m,n]/m.本文主要目的是研究这两个新的函数的渐近性质,利用解析方法得到这两个函数的几个渐近公式.     

Oscillations of Error Terms Associated with Certain Arithmetical Functions

We prove a general theorem on oscillatory properties of error terms associated with real arithmetical functions whose Mellin transform may have singularities with several summands containing arbitrary complex powers and logarithmic polynomials. The theorem generalizes a theorem of J. Kaczorowski and J. Pintz and is motivated by the applications to algebraic integers with factorizations of distinct lengths. An application of the theorem to the study of the Hilbert semigroup modulo 5 is presented.     

A Class of Rational Arithmetical Functions with Combinatorial Meanings

ＡＣｌａｓｏｆＲａｔｉｏｎａｌＡｒｉｔｈｍｅｔｉｃａｌＦｕｎｃｔｉｏｎｓｗｉｔｈＣｏｍｂｉｎａｔｏｒｉａｌＭｅａｎｉｎｇｓＰｅｎｔｉＨａｕｋｋａｎｅｎ（Ｄｅｐｔ．ｏｆＭａｔｈ．Ｓｃｉｓ．，Ｕｎｉｖ．ｏｆＴａｍｐｅｒｅ，Ｐ．Ｏ．Ｂｏｘ６０７，ＦＩＮ－...     

一类有理算术函数及其组合意义（英）

An arithmetical function f is said to be a rational arithmetical function of order (s,r) if there existcompletely multiplicative functions f₁,f₂,…,f_s and g₁,g₂,…,g_r such thatf=f₁*f₂*… *f_s*(g₁)^-1*(g₂)^-1*… *(g_r) -1 ,where * is the Dirichlet convolution. Recently, L.C. Hsu and Wang Jun studied combinatorial meanings of rational arithmetical functions of order (1,r) . We study these meanings in the setting of Narkiewicz's regular convolution.     

On Some Rings of Arithmetical Functions

In this paper, we consider several constructions which from a given B-product * _B lead to another one We shall be interested in finding what algebraic properties of the ring are shared also by the ring . In particular, for some constructions the rings R _B and will be isomorphic and therefore have the same algebraic properties.     

On the Mean Square of the Error Terms Corresponding to Exponential Sums Involving the Ideal Counting Function

In this paper we consider the asymptotic behaviour of the error term Q(x;h/q), which is defined by (1.2). In particular, we derive a certain lower bound estimate of this function when h, k and q are fixed integers, and study the non-trivial upper bound estimates of the mean value of Q(x;h/q).     

2SUR回归模型系数估计的均方误差比较

对于2SUR回归模型的参数估计问题,给出了一些一航均方误差矩阵比较结果,据此提出了一类线性估计和一类基于离差阵广义非限定估计的非线性两步估计,并获得了该两步估计类的一些有限样本性质。     

On a Class of Integer-Valued Functions

The paper deals with the class of entire functions that increase not faster than exp{γ∣z∣^6/5(ln∣z∣)^?1} and that, together with their first derivatives, take values from a fixed field of algebraic numbers at the points of a two-dimensional lattice of general form (in this case, the values increase not too fast). It is shown that any such functions is either a polynomial or can be represented in the form e^?mαzP(e^αz), where m is a nonnegative integer, P is a polynomial, and α is an algebraic number.

     

关于一类单叶函数

A sharp coefficient estimate,distortion theorem and the radius of convexityare determined for the class R(α,β,A,B) of function f(z)=z+(?)a_nzⁿ satisfyingthe condition |(f′(z)-1)/(Bf′(z)-[B+(A-B)(1-α)])|<β for some α,β(0≤α<1,0<β≤1) and -1≤A相似文献   

On the Mean Value of the Square of a Generalized Dedekind Sum

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

关于一类函数单调性的再讨论

针对函数F(x)=x∫0(x-ct)f(t)dt的单调性,通过反例说明某文献的相关论述存在错误,并给出命题,全面讨论此类函数在各种情况下的单调性.     

关于Dedekind和的均值公式

本文的主要目的是利用ＤｉｒｉｃｈｌｅｔＬ－函数的均值定理研究Ｄｅｄｅｋｉｎｄ和的值分布性质，并给出一个较强的均值公式．     

回归系数线性函数的均方相合估计——问题与猜测

设有线性模型 Y_i=x′_iβ+e_i,i=1,…,n,… (1) 其中{x_i}为已知的p维向量,β为未知的p维向量,{e_i}为随机误差序列。以β_π记β的基于(1)的前n个观测值Y_1,…,Y_π的最小二乘估计(LSE)。在[1]中,我们曾建立如下的结果:     

关于面积平均p叶函数（Ⅱ）

假设ｆ（ｚ）＝ｚ＾ｐ（１＋Σ＾∞ｎ＝１ａｎ＾ｚ＾ｎｋ）是△＝｛｜ｚ｜＜１｝内面积平均ｐ叶的（如果必要，△＝｛｜ｚ｜＜１｝＼（－１，０］）。本文的主要结论是：（１）如果设Ｍ（ｒ）＝ｍａｘ｜ｆ（ｚ）｜，则（１－ｒ）２ｐ／ｋＭ（ｒ）→αｋ≤１（ｒ→１），αｋ＝１的充要条件是ｆ（ｚ）＝ｚ＾ｐ（１－ｘｚ＾ｋ）＾－２ｐ／ｋ，｜ｘ｜＝１。进一步，如果１≤ｋ＜４ｐ，我们有｜ａｎ｜ｎ＾１－２ｐ／ｋ→αｋГ（２ｐ／ｋ     

关于一类p叶解析函数

本文考虑了函数类Tσ（p,a)闭凸包极值点,并用它确定系数估计。对函数类Tσ（p,a)的其它一些有趣性质也进行也研究。