scholarly journals Joint universality of some zeta-functions. I

2010 ◽  
Vol 51 ◽  
Author(s):  
Santa Račkauskienė ◽  
Darius Šiaučiūnas
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Zeta Functions ◽  
Joint Universality ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

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.

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.

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 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 SELF-APPROXIMATION FOR THE RIEMANN ZETA FUNCTION

2012 ◽  
Vol 87 (3) ◽  
pp. 452-461 ◽  
Author(s):  
TAKASHI NAKAMURA ◽  
ŁUKASZ PAŃKOWSKI
Keyword(s):  
Zeta Function ◽  
Half Plane ◽  
Riemann Zeta Function ◽  
Critical Strip ◽  
Approximation Of Functions ◽  
Joint Universality ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
The Right

AbstractIn the paper we deal with self-approximation of the Riemann zeta function in the half plane $\operatorname {Re} s\gt 1$ and in the right half of the critical strip. We also prove some results concerning joint universality and joint value approximation of functions $\zeta (s+\lambda +id\tau )$ and $\zeta (s+i\tau )$.

Simultaneous Polynomial Approximations of the Lerch Function

2009 ◽  
Vol 61 (6) ◽  
pp. 1341-1356 ◽  
Author(s):  
Tanguy Rivoal
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Zeta Functions ◽  
Detailed Comparison ◽  
Padé Approximants ◽  
Bivariate Polynomial ◽  
Integer Points ◽  
Polynomial Approximations ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

Abstract We construct bivariate polynomial approximations of the Lerch function that for certain specialisations of the variables and parameters turn out to be Hermite–Padé approximants either of the polylogarithms or ofHurwitz zeta functions. In the former case, we recover known results, while in the latter the results are new and generalise some recent works of Beukers and Prévost. Finally, we make a detailed comparison of our work with Beukers’. Such constructions are useful in the arithmetical study of the values of the Riemann zeta function at integer points and of the Kubota–Leopold p-adic zeta function.

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