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1.
关于Genocchi数和Riemann Zeta-函数的一些恒等式   总被引:11,自引:0,他引:11  
利用计算技巧给出了由Genocci数和RiemannZeta-函数组成的和式的递归关系,得到了一些关于Genocchi数和RiemannZeta-函数的恒等式  相似文献
2.
一类Genocchi数与Riemann Zeta函数多重求和的计算公式   总被引:7,自引:0,他引:7       下载免费PDF全文
本文利用计算技巧建立Genocchi数Gn与Riemann Zeta函数ζ(2n)多重求和的一般结果,推广王大明,张祥德^[5]的结果。  相似文献
3.
关于Genocchi数和Riemann Zeta-函数的一些恒等式   总被引:4,自引:2,他引:2       下载免费PDF全文
利用计算技巧给出了由Genocci数和Ricmann Zeta-函数组成的和式的递归关系,得到了一些关于Genocchi Zeta-函数的恒等式。  相似文献
4.
Product of Uniform Distribution and Stirling Numbers of the First Kind   总被引:3,自引:0,他引:3  
Let Vk=u1u2……uk, ui's be i.i.d - U(0, 1), the p.d.f of 1 - Vk+l be the GF of the unsigned Stirling numbers of the first kind s(n, k). This paper discusses the applications of uniform distribution to combinatorial analysis and Riemann zeta function; several identities of Stifling series are established, and the Euler's result for ∑ Hn/n^k-l, k ≥ 3 is given a new probabilistic proof.  相似文献
5.
Vinogradov's Integral and Bounds for the Riemann Zeta Function   总被引:2,自引:0,他引:2  
The main result is an upper bound for the Riemann zeta functionin the critical strip: with A = 76.2 and B = 4.45, valid for 1 and |t| 3. The previousbest constant B was 18.5. Tools include a variant of the Korobov–Vinogradovmethod of bounding exponential sums, an explicit version ofT. D. Wooley's bounds for Vinogradov's integral, and explicitbounds for mean values of exponential sums over numbers withoutsmall prime factors, also using methods of Wooley. An auxiliaryresult is the exponential sum bound , where N is a positive integer, t is a real number, = log (t)/(logN) and 2000 Mathematical Subject Classification: primary 11M06, 11N05,11L15; secondary 11D72, 11M35.  相似文献
6.
Simple Zeros of the Riemann Zeta-Function   总被引:1,自引:0,他引:1  
Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.  相似文献
7.
对偶形式的Hardy不等式的加强改进   总被引:1,自引:0,他引:1  
黄启亮  杨必成 《数学杂志》2005,25(3):307-311
对p>1的对偶形式的Hardy不等式,采用权系数的方法,建立一个联系正实轴上Riemann-ζ函数的加强不等式.  相似文献
8.
一类新的包含Riemann Zeta函数的求和计算公式   总被引:1,自引:0,他引:1  
1引 言 本文ζ(s)表示Riemann Zeta函数,当Re(s)>1时,ζ(s)=sum from n=1to∞(1/n~s).包含ζ(s)的形如  相似文献
9.
一类扩展Euler和的表示问题   总被引:1,自引:0,他引:1  
应用Parseval定理和Nielsen广义多重对数函数的性质,给出了非线性扩展Euler和的Riemann Zeta函数表示.对来自于实验数学中的扩展Euler和∑n=1∞H2n/n2的经验公式给出了严格的理论证明.此方法也适用于求其它扩展Euler和的计算问题.  相似文献
10.
Zeta-nonlocal scalar fields   总被引:1,自引:0,他引:1  
We consider some nonlocal and nonpolynomial scalar field models originating from p-adic string theory. An infinite number of space-time derivatives is determined by the operator-valued Riemann zeta function through the d’Alembertian □ in its argument. The construction of the corresponding Lagrangians L starts with the exact Lagrangian for the effective field of the p-adic tachyon string, which is generalized by replacing p with an arbitrary natural number n and then summing over all n. We obtain several basic classical properties of these fields. In particular, we study some solutions of the equations of motion and their tachyon spectra. The field theory with Riemann zeta-function dynamics is also interesting in itself. Dedicated to Vasilii Sergeevich Vladimirov on his 85th birthday __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 3, pp. 364–372, December, 2008.  相似文献
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