共查询到20条相似文献,搜索用时 15 毫秒
1.
This is a survey of results on joint universality in Voroninʼs sense of various zeta-functions, when in the collection of these functions some of them have the Euler product and the others have not. 相似文献
2.
In the paper, the zeta-functions of finite Abelian groups of rank 2 and 3 are considered. One- and two-dimensional limit theorems for these zeta-functions on the complex plane and in the space of meromorphic functions are obtained. 相似文献
3.
We study twists of the Lerch zeta-functions with shifted Dirichlet characters. This generalizes Dirichlet L-functions. These twists turn out to be meromorphic with at most one simple pole and satisfy a functional equation (similar to the functional equation of the Lerch zeta-function) if the Dirichlet character is primitive. We also investigate the distributions of their zeros. In particular, we disprove the analogue of Riemann's hypothesis for some twists. 相似文献
4.
We prove a joint universality theorem for general Dirichlet series. The conditions of this theorem are weaker than those in [7]. 相似文献
5.
A. Laurinčikas 《Lithuanian Mathematical Journal》2008,48(1):79-91
We prove a joint universality theorem for a collection of periodic Hurwitz zeta-functions with algebraically independent parameters
over the field of rational numbers. 相似文献
6.
We give corrected statements of some theorems from [5] and [6] on joint value-distribution of Lerch zeta-functions (limit
theorems, universality, functional independence). We also present a new direct proof of a joint limit theorem in the space
of analytic functions and an extension of a joint universality theorem.
Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 3, pp. 332–350, July–September, 2006. 相似文献
7.
A. Laurinčikas 《Lithuanian Mathematical Journal》2000,40(2):135-139
In the paper one way of the effectivization of the universality theorem for the Lerch zeta-function is discussed. It is based
on the estimate of the rate of convergence in a limit theorem in the space of analytic functions.
Partially supported by the Lithuanian State Science and Studies Foundation.
Translated from Lietuvos Matematikos Rinkinys, Vol. 40, No. 2, pp. 172–178, April–June, 2000.
Translated by A. Laurinčikas 相似文献
8.
Ibrahim A. Abou-tair 《Applicable analysis》2013,92(1-4):205-219
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 相似文献
9.
Pablo Andrés Panzone 《Integral Transforms and Special Functions》2018,29(11):893-908
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. 相似文献
10.
In this paper, we prove a joint limit theorem for the Riemann zeta-function in the space of analytic functions in the sense of weak convergence of probability measures. 相似文献
11.
A discrete limit theorem for the Lerch zeta-function with an integer parameter in the space of meromorphic functions is proved. 相似文献
12.
In this paper, a joint limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for general Dirichlet series is proved. The explicit form of the limit measure is given. 相似文献
13.
In the paper, the explicit form of the limit measure in a joint limit theorem for the Riemann zeta-function in the space of analytic functions is given. 相似文献
14.
In the paper, a discrete limit theorem in the sense of the weak convergence of probability measures for the Matsumoto zeta-function on the complex plane is proved. 相似文献
15.
A connection is established between the fractional moments of the Riemann zeta-function and the number of its zeros on the critical line. 相似文献
16.
R. Macaitienė 《Lithuanian Mathematical Journal》2005,45(1):84-93
We prove joint discrete limit theorems in the sense of weak convergence of probability measures in the space of analytic functions for general Dirichlet series.__________Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 1, pp. 104–116, January–March, 2005.Translated by R. Macaitien 相似文献
17.
We prove a joint discrete limit theorem in the sense of weak convergence on the complex plane for general Dirichlet series. 相似文献
18.
We obtain a joint limit theorem in the sense of weak convergence of probability measures for general Dirichlet series in the space of meromorphic functions. 相似文献
19.
We prove a joint two-dimensional limit theorem in the sense of weak convergence of probability measures on the complex plane for general Dirichlet series. 相似文献
20.
We prove a discrete limit theorem for general Dirichlet series in the sense of weak convergence of probability measures in the space of analytic funtions. Examples are presented. 相似文献