The joint value-distribution of the Riemann zeta function and Hurwitz zeta functions

2007 ◽  
Vol 47 (1) ◽  
pp. 32-47 ◽  
Author(s):  
H. Mishou
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Zeta Functions ◽  
Value Distribution ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

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.

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.

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.

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.

Value Distribution of the Riemann Zeta Function

2008 ◽  
Vol 51 (3) ◽  
pp. 334-336
Author(s):  
I. Ascah-Coallier ◽  
P. M. Gauthier
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Short Proof ◽  
Value Distribution ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

AbstractIn this note, we give a new short proof of the fact, recently discovered by Ye, that all (finite) values are equidistributed by the Riemann zeta function.

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