一个二元丢番图不等式

本文证明了如果1相似文献   

一个素变数丢番图不等式

本文证明了如果1相似文献   

一个素变数的Diophantine不等式

设１＜Ｃ＜１３／１２．本文证明了存在Ｎ（Ｃ）＞０使得对任意实数Ｎ＞Ｎ（Ｃ），下面的不等式｜＋＋　－Ｎ｜＜Ｎ－　　　　）ｌｏｇｓＮ有素数解ｐ１，ｐ２，ｐ３，其中ｓ＝２（１５）．     

On two Diophantine inequalities over primes

Let $1<c<37∕18,c\ne 2$ and $N$ be a sufficiently large real number. In this paper, we prove that, for almost all $R\in (N,2N]$, the Diophantine inequality $|p_1^c+p_2^c+p_3^c?R|<{log}^{?1}N$ is solvable in primes $p_1,p_2,p_3$. Moreover, we also investigate the problem of six primes and prove that the Diophantine inequality $|p_1^c+p_2^c+p_3^c+p_4^c+p_5^c+p_6^c?N|<{log}^{?1}N$ is solvable in primes $p_1,p_2,p_3,p_4,p_5,p_6$ for sufficiently large real number $N$.     

一个素变数丢番图不等式

本文证明了如果１＜ｃ＜２３７／２１４，则对于充分大的Ｎ和ε≥Ｎ－１／５（２３７／２１４－ｃ）＋ｖ（ｖ＞０）表达式Ｄ（Ｎ）：＝Σ｜ｐｃ１＋ｐｃ２＋ｐｃ３－Ｎ｜＜－εｌｏｇｐ１ｌｏｇｐ２ｌｏｇｐ３ 关于素变数ｐ１，ｐ２，ｐ３有渐近公式，改进了文献［１］的结果１＜Ｃ＜１．１．     

一个素变数丢番图方程

证明了如果 １＜ｃ＜２５８／２３５，则素变数丢番图方程对充分大的 Ｎ是可解的，改进了 Ｋｕｍｃｈｅｖ和 Ｎｅｄｅｖａ的结果 １＜ｃ＜１２／１１．     

有关殆素数的二元丢番图不等式

Pr表示最多r个素因子的正整数.作者证明了,对于任一足够大的实数N和1＜c＜c0,不等式|pc+Pcr-N|＜N9/10(1-c0/c)对素数p和Pr是可解的.特别地,当1＜c＜c0=1.03074432…,有r=6.这个结果改进了翟文广和曹晓东的结果.     

Formulas for the Riemann zeta-function and certain Dirichlet series

Using known theta identities and formulas of S. Ramanujan and G. Hardy among others we prove several formulas for the Riemann zeta-function and two Dirichlet series.     

AbsoluteN qα -summability of the series conjugate to a Fourier series

The object of the paper is to study the absolute N_qα-summability of the series conjugate to a Fourier series, generalising a known result.     

Approximation of integrable functions by general linear operators of their fourier series

The pointwise estimates of the deviation T n,A,B f (·) f (·) in terms of moduli of continuity .f and w.f there are proved. Analogical results on norm approximation with remarks and corollaries are also given. In the results there are used the essentially weaker conditions than these in [Mittal, M. L.: J. Math. Anal. Appl., 220, 434-450 (1998) Theorem 1, p. 437].     

The study of the fourier series of functions defined on moran fractals

LetE be a Moran fractal andH ^s (E) denote thes-dimensional Hausdorff measure ofE. In this paper, we define a orthonormal and complete system of functions in the Hilbert spaceL ²(E,H ^s ) and prove that partial sums of the Fourier series, with respect to , of each functionf(x)L ¹(E,H ^s ) converge tof(x) atH ^s -a.e.xE. Moreover, the Fourier series off, forfL ^p (E,H ^s ),p1, converges off inL ^p -norm. When Moran fractals degenerate into self-similar fractals, our results well agree with M. Reyes's results.This work is supported in part by the National Natural Science Foundation of China.     

On the degree of approximation of functions belonging to a Lipschitz class by Hausdorff means of its fourier series

In a recent paper Lal and Yadov [4] obtained a theorem on the degree of approximation for a function belonging to the Lipschitz class Lipα using the product of the Cesàro and Euler means of order one of its Fourier series. In this paper we extend this result to any regular Hausdorff matrix for the same class of functions.     

Multipliers for the absolute euler summability of fourier series

In this paper, the author has investigated necessary and sufficient conditions for the absolute Euler summability of the Fourier series with miltipliers. These conditions are weaker than those obtained earlier by some workers. It is further shown that the multipliers are best possible in certain sense.     

On summability of eigenfunction expansions of piecewise smooth functions

We consider two forms of eigenfunction expansions associated with an arbitrary elliptic differential operator with constant coefficients and order m, that is the multiple Fourier series and integrals. For the multiple Fourier integrals, we prove the convergence of the Riesz means of order s?>?(N???3)/2 of piecewise smooth functions of N?≥?2 variables. The same result is proved in the case of the N?≥?3 dimensional multiple Fourier series.     

On a certain class of dirichlet series

For 0 1, let L(s,a) and L?(s,a) be the Dirichlet series L(s,a) = ∑ : cos (2πna)n^-s and L? [001](s,a) = ∑ sin (2πna)n^-s. We show that L(s,a) and L?(s,a[001]) have holomorphic extension in the whole complex plane. Values of L(s,a)andL?(s,a) at the negative integers are given. Moreover values of L?(s,a) at the intergers 0,2,4,... and values of L^?(s,a)at the integers 1,3,5,... are obtained. An exponential sums of certain recursion formulas are obtained by means of bernoulli numbers and Bernoulli polynomials     

Concerning the multiplicators of Fourier series in the trigonometric system

In this paper we prove theorems on multiplicators of Fourier series inL _p, where the conditions depend on a parameterp. An example illustrating the importance of these conditions is constructed. Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 235–247, February, 1998.     

On the Diophantine equation

Let be an odd prime. In this paper, using some theorems of Adachi and the author, we prove that if and , then the equation , and the equation , have no integral solutions respectively. Here is th Bernoulli number.

     

On pointwise convergence of Fourier series of radial functions in several variables

We prove the pointwise convergence of the Fourier series for radial functions in several variables, which in the case is the Dirichlet-Jordan theorem itself. In our proof the method for the case of the indicator function of the ball is very useful.

     

On vector-valued random Fourier series

Consider a (complex) Banach spaceX, such thatX C_O, and vectors(X _i ) _i ofX. Consider an independent standard normal sequence(g _i ) _i . Then if anX-valued random Fourier series _{|k| n} e ^ikt g _k x _k satisfies