Results 11 to 20 of about 1,892 (123)

Universality of the Periodic Hurwitz Zeta-Function with Rational Parameter

Siberian Mathematical Journal, 2018
Voronin's theorem from 1975 states that the Riemann zeta function is universal in the sense that its shifts approximate a wide class of analytic functions. More precisely, let \(\mathscr{K}\) be the class of compact subsets of the strip \(D=\left\{s \in \mathbb{C}: \frac{1}{2}
Laurinčikas, A., Macaitienė, R., Mochov, D., Šiaučiūnas, D.   +3 more
openaire   +3 more sources

A Modification of the Mixed Joint Universality Theorem for a Class of Zeta Functions

Mathematics, 2022
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 an accuracy of ε>0 by suitable vertical shifts of the pair consisting the Riemann and ...
Roma Kačinskaitė, Benjaminas Togobickij   +1 more
doaj   +1 more source

Joint universality of some zeta-functions. I

Lietuvos Matematikos Rinkinys, 2010
In the paper, the joint universality for the Riemann zeta-function and a collection of periodic Hurwitz zeta functions is discussed and basic results are given.
Santa Račkauskienė, Darius Šiaučiūnas   +1 more
doaj   +1 more source

A mixed joint universality theorem for zeta‐functions

Mathematical Modelling and Analysis, 2010
In the paper, a joint universality theorem for the Riemann zeta‐function and a collection of periodic Hurwitz zeta‐functions on approximation of analytic functions is obtained.
Jonas Genys, Renata Macaitienė, Santa Račkauskienė, Darius Šiaučiūnas   +3 more
doaj   +1 more source

A Mixed Joint Universality Theorem for Zeta-Functions. II

Mathematical Modelling and Analysis, 2014
In the paper, a joint universality theorem on the approximation of analytic functions for zeta-function of a normalized Hecke eigen cusp form and a collection of periodic Hurwitz zeta-functions with algebraically independent parameters is obtained.
Vaida Pocevičienė, Darius Šiaučiūnas   +1 more
doaj   +1 more source

The Lerch Zeta Function II. Analytic Continuation [PDF]

, 2010
This is the second of four papers that study algebraic and analytic structures associated with the Lerch zeta function. In this paper we analytically continue it as a function of three complex variables.
Apostol T. M., Barnes E. W., Berndt B., Hurwitz A., Lipschitz M., Lipschitz M., Mikolas M., Oberhettinger E.   +7 more
core   +1 more source

Questions around the nontrivial zeros of the Riemann zeta-function. Computations and classifications

Mathematical Modelling and Analysis, 2011
We study the sequence of nontrivial zeros of the Riemann zeta-function with respect to sequences of zeros of other related functions, namely, the Hurwitz zeta-function and the derivative of Riemann's zeta-function.
Ramūnas Garunkštis, Joern Steuding
doaj   +1 more source

Applications of the Mellin-Barnes integral representation [PDF]

, 1995
We apply the Mellin-Barnes integral representation to several situations of interest in mathematical-physics. At the purely mathematical level, we derive useful asymptotic expansions of different zeta-functions and partition functions.
Actor A, Actor A, Actor A, Actor A, Actor A, Actor A, Andrews G E, Belavin A, Bender C M, Bernard C W, Bleistein N, Buchbinder I L, Casimir H B G, Copson E T, Critchley R, Denardo G, Dowker J S, Duistermaat J J, E Elizalde, Elizalde E, Elizalde E, Elizalde E, Elizalde E, Elizalde E, Elizalde E, Erdelyi A, Goncharov Y P, Gradshteyn I S, Hawking S W, Hejhal D A, Jorgenson J, K Kirsten, Kapusta J I, Kirsten K, La Veque W J, McLachlan A, McLachlan A, Meinardus G, Meinardus G, Olver F W J, Ray D B, S Zerbini, Seeley R T, Toms D J, Voros A, Wolpert S A   +45 more
core   +2 more sources

A discrete limit theorem for the periodic Hurwitz zeta-function

Lietuvos Matematikos Rinkinys, 2015
In the paper, we prove a limit theorem of discrete type on the weak convergence of probability measures on the complex plane for the periodic Hurwitz zeta-function.
Audronė Rimkevičienė
doaj   +1 more source

On mixed joint discrete universality for a class of zeta-functions: a further generalization

Mathematical Modelling and Analysis, 2020
We present the most general at this moment results on the discrete mixed joint value-distribution (Theorems 5 and 6) and the universality property (Theorems 3 and 4) for the class of Matsumoto zeta-functions and periodic Hurwitz zeta-functions under ...
Roma Kačinskaitė, Kohji Matsumoto
doaj   +1 more source