scholarly journals Approximation of Analytic Functions by Shifts of Certain Compositions

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2583
Author(s):  
Darius Šiaučiūnas ◽  
Raivydas Šimėnas ◽  
Monika Tekorė
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Analytic Functions ◽  
Zeta Functions ◽  
Multidimensional Space ◽  
Space Of Analytic Functions ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

In the paper, we obtain universality theorems for compositions of some classes of operators in multidimensional space of analytic functions with a collection of periodic zeta-functions. The used shifts of periodic zeta-functions involve the sequence of imaginary parts of non-trivial zeros of the Riemann zeta-function.

scholarly journals UNIVERSALITY OF ZETA-FUNCTIONS OF CUSP FORMS AND NON-TRIVIAL ZEROS OF THE RIEMANN ZETA-FUNCTION

2021 ◽  
Vol 26 (1) ◽  
pp. 82-93
Author(s):  
Aidas Balčiūnas ◽  
Violeta Franckevič ◽  
Virginija Garbaliauskienė ◽  
Renata Macaitienė ◽  
Audronė Rimkevičienė
Keyword(s):  
Zeta Function ◽  
Wide Class ◽  
Riemann Zeta Function ◽  
Analytic Functions ◽  
Pair Correlation ◽  
Zeta Functions ◽  
Weak Form ◽  
Cusp Forms ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

It is known that zeta-functions ζ(s,F) of normalized Hecke-eigen cusp forms F are universal in the Voronin sense, i.e., their shifts ζ(s + iτ,F), τ R, approximate a wide class of analytic functions. In the paper, under a weak form of the Montgomery pair correlation conjecture, it is proved that the shifts ζ(s+iγkh,F), where γ1 < γ2 < ... is a sequence of imaginary parts of non-trivial zeros of the Riemann zeta function and h > 0, also approximate a wide class of analytic functions.

scholarly journals ON DISCRETE UNIVERSALITY OF COMPOSITE FUNCTIONS

2012 ◽  
Vol 17 (2) ◽  
pp. 271-280 ◽  
Author(s):  
Jovita Rašytė
Keyword(s):  
Analytic Function ◽  
Zeta Function ◽  
Riemann Zeta Function ◽  
Analytic Functions ◽  
Space Of Analytic Functions ◽  
Composite Functions ◽  
The Riemann Zeta Function ◽  
Fixed Positive Number ◽  
Riemann Zeta ◽  
Discrete Universality

In 1975, S.M. Voronin proved that the Riemann zeta-function ζ (s) is universal in the sense that its shifts approximate uniformly on some sets any analytic function. Let h be a fixed positive number such that exp is irrational for all . In the paper, the classes of functions F such that the shifts F (ζ (s + imh)), , approximate any analytic function are presented. For the proof of theorems, some elements of the space of analytic functions are applied.

scholarly journals A Two-Dimentional Discrete Limit Theorem in the Space of Analytic Functions for Mellin Transforms of the Riemann Zeta-Function

2008 ◽  
Vol 13 (2) ◽  
pp. 159-167 ◽  
Author(s):  
V. Balinskaitė ◽  
V. Laurinčikas
Keyword(s):  
Limit Theorem ◽  
Zeta Function ◽  
Riemann Zeta Function ◽  
Analytic Functions ◽  
Critical Line ◽  
Space Of Analytic Functions ◽  
Mellin Transforms ◽  
Convergence Of Probability Measures ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

In the paper, a two-dimentional discrete limit theorem in the sense of weak convergence of probability measures in the space of analytic functions for Mellin transforms of the Riemann zeta-function on the critical line is obtained.

scholarly journals JOINT DISCRETE APPROXIMATION OF A PAIR OF ANALYTIC FUNCTIONS BY PERIODIC ZETA-FUNCTIONS

2020 ◽  
Vol 25 (1) ◽  
pp. 71-87 ◽  
Author(s):  
Aidas Balčiūnas ◽  
Virginija Garbaliauskienė ◽  
Julija Karaliūnaitė ◽  
Renata Macaitienė ◽  
Jurgita Petuškinaitė ◽  
...  
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Analytic Functions ◽  
Simultaneous Approximation ◽  
Pair Correlation ◽  
Zeta Functions ◽  
Weak Form ◽  
Approximation Theorems ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

In the paper, the problem of simultaneous approximation of a pair of analytic functions by a pair of discrete shifts of the periodic and periodic Hurwitz zeta-function is considered. The above shifts are defined by using the sequence of imaginary parts of non-trivial zeros of the Riemann zeta-function. For the proof of approximation theorems, a weak form of the Montgomery pair correlation conjecture is applied.

A MIXED JOINT UNIVERSALITY THEOREM FOR ZETA‐FUNCTIONS

2010 ◽  
Vol 15 (4) ◽  
pp. 431-446 ◽  
Author(s):  
Jonas Genys ◽  
Renata Macaitienė ◽  
Santa Račkauskienė ◽  
Darius Šiaučiūnas
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Analytic Functions ◽  
Zeta Functions ◽  
Joint Universality ◽  
Universality Theorem ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Joint Universality Theorem

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.

scholarly journals Joint universality of the Riemann zeta-function and Lerch zeta-functions

2013 ◽  
Vol 18 (3) ◽  
pp. 314-326
Author(s):  
Antanas Laurinčikas ◽  
Renata Macaitienė˙
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Zeta Functions ◽  
Rational Numbers ◽  
Joint Universality ◽  
Universality Theorem ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Joint Universality Theorem

In the paper, we prove a joint universality theorem for the Riemann zeta-function and a collection of Lerch zeta-functions with parameters algebraically independent over the field of rational numbers.

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