Joint universality of Hurwitz zeta-functions and nontrivial zeros of the Riemann zeta-function

Abstract

In 2017, Garunkštis, Laurinčikas and Macaitienė proved the discrete universality theorem for the Riemann zeta-function sifted by the nontrivial zeros of the Riemann zetafunction. This discrete universality has been extended in various zeta-functions and L-functions. In this paper, we generalize this discrete universality for Matsumoto zeta-functions.

Joint Discrete Approximation of Analytic Functions by Hurwitz Zeta-Functions

“…• is a sequence of imaginary parts of non-trivial zeros of the Riemann zeta-function were applied in [3,23,26] and [32]. Analogical universality theorems for the function ζ(s, α; a) were proved in [11,29,31], and follow from joint universality theorems for periodic zetafunctions (see, for example, [12,14,17,22,25,30]).…”

Joint Discrete Approximation of a Pair of Analytic Functions by Periodic Zeta-Functions

“…The Montgomery conjecture gives the asymptotic formula for the left-hand side of (1.4). The condition (1.4) was applied in [6] for the approximation of analytic functions by shifts ζ(s + iγ k h), in [30] for shifts ζ(s + iγ n h, α) and by shifts (ζ(s + iγ k h), ζ(s + iγ k h, α))) in [21]. In [4,5], in place of (1.4), the Riemann hypothesis was used.…”

Joint universality of periodic zeta-functions with multiplicative coefficients. II

“…and its meromorphic continuation are called the periodic Hurwitz zeta-function. In [15] and [3], under hypothesis (1), joint universality theorems involving sequence {γ k } for the pair consisting from the Riemann and Hurwitz zeta-functions and their periodic analogues, respectively, were obtained, while in [23], such theorems were proved for Hurwitz zeta-functions.…”