相关论文: On mixed joint discrete universality for a class o…

We give a new type of mixed discrete joint universality properties, which is satisfied by a wide class of zeta-functions. We study the universality for a certain modification of a Matsumoto zeta-function and a periodic Hurwitz zeta-function…

We prove a new case of mixed discrete joint universality theorem on approximation of certain target couple of analytic functions by the shifts of a pair consisting of the function belonging to wide class of Matsumoto zeta-functions and the…

We present the most general at this moment results on the discrete mixed joint value-distribution and the universality property for the class of Matsumoto zeta-functions and periodic Hurwitz zeta-functions under certain linear independence…

Two remarks related with the mixed joint universality for a polynomial Euler product and a periodic Hurwitz zeta-function with a transcendental parameter are given. One is the mixed joint functional independence, and the other is a…

We prove a mixed joint discrete universality theorem for a Matsumoto zeta-function $\varphi(s)$ (belonging to the Steuding subclass) and a periodic Hurwitz zeta-function $\zeta(s,\alpha;{\mathfrak{B}})$. For this purpose, certain…

We study analytic properties of multiple zeta-functions of generalized Hurwitz-Lerch type. First, as a special type of them, we consider multiple zeta-functions of generalized Euler-Zagier-Lerch type and investigate their analytic…

In 2017, Garunk\v{s}tis, Laurin\v{c}ikas and Macaitien\.{e} proved the discrete universality theorem for the Riemann zeta-function sifted by the nontrivial zeros of the Riemann zeta-function. This discrete universality has been extended in…

The property of zeta-functions on mixed joint universality in the Voronin's sense states that any two holomorphic functions can be approximated simultaneously with accuracy $\epsilon>0$ by suitable vertical shifts of the pair consisting…

In 2003, Garunk\v{s}tis provided a lower bound for the lower density of the universality theorem for the Riemann zeta-function. In this paper, we generalize this result for the hybrid joint universality theorem for Dirichlet $L$-functions…

We study the values taken by the Riemann zeta-function $\zeta$ on discrete sets. We show that infinite vertical arithmetic progressions are uniquely determined by the values of $\zeta$ taken on this set. Moreover, we prove a joint discrete…

Finite Euler product is known to be one of the classical zeta functions in number theory. In [1], [2] and [3], we have introduced some multivariable zeta functions and studied their definable probability distributions on R^d. They include…

Analytic properties of three types of multiple zeta functions, that is, the Euler-Zagier type, the Mordell-Tornheim type and the Apostol-Vu type have been studied by a lot of authors. In particular, in the study of multiple zeta functions…

The main aim of this paper is to give a new generalization of Hurwitz-Lerch Zeta function of two variables.Also, we investigate several interesting properties such as integral representations, summation formula and a connection with…

In 1975 Voronin proved the universality theorem for the Riemann zeta-function $\zeta(s)$ which roughly says that any admissible function $f(s)$ is approximated by $\zeta(s)$. A few years later Reich proved a discrete analogue of this…

We study rather general multiple zeta-functions whose denominators are given by polynomials. The main aim is to prove explicit formulas for the values of those multiple zeta-functions at non-positive integer points. We first treat the case…

We prove some uniqueness results for the Riemann zeta-function and the Euler gamma-function by virtue of shared values using the value distribution theory.

In the present paper, we treat multidimensional polynomial Euler products with complex coefficients on ${\mathbb{R}}^d$. We give necessary and sufficient conditions for the multidimensional polynomial Euler products to generate infinitely…

For $0<\alpha, \lambda \leq 1$, the Lerch zeta-function is defined by $L(s;\alpha, \lambda)$$:= \sum_{n=0}^\infty e^{2\pi i\lambda n} (n+\alpha)^{-s}$, where $\sigma>1$. In this paper, we prove joint universality for Lerch zeta-functions…

In 1979, Gonek presented the hybrid joint universality theorem for Dirichlet $L$-functions and proved the universality theorem for Hurwitz zeta-functions with rational parameter as an application. Following the introduction of the hybrid…

We introduce Schur multiple zeta functions which interpolate both the multiple zeta and multiple zeta-star functions of the Euler-Zagier type combinatorially. We first study their basic properties including a region of absolute convergence…