scholarly journals Joint Universality of the Zeta-Functions of Cusp Forms

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2161
Author(s):  
Renata Macaitienė
Keyword(s):  
Cusp Form ◽  
Modular Group ◽  
Zeta Functions ◽  
Rational Numbers ◽  
Cusp Forms ◽  
Algebraic Numbers ◽  
Joint Universality ◽  
Universality Theorem ◽  
Linearly Independent ◽  
Joint Universality Theorem

Let F be the normalized Hecke-eigen cusp form for the full modular group and ζ(s,F) be the corresponding zeta-function. In the paper, the joint universality theorem on the approximation of a collection of analytic functions by shifts (ζ(s+ih1τ,F),⋯,ζ(s+ihrτ,F)) is proved. Here, h1,⋯,hr are algebraic numbers linearly independent over the field of rational numbers.

scholarly journals The joint universality and the functional independence for Lerch zeta-functions

2000 ◽  
Vol 157 ◽  
pp. 211-227 ◽  
Author(s):  
Antanas Laurinčikas ◽  
Kohji Matsumoto
Keyword(s):  
Zeta Functions ◽  
Rational Numbers ◽  
Functional Independence ◽  
Joint Universality ◽  
Universality Theorem ◽  
Transcendental Numbers ◽  
Joint Universality Theorem

The joint universality theorem for Lerch zeta-functions L(λl, αl, s) (1 ≤ l ≤ n) is proved, in the case when λls are rational numbers and αls are transcendental numbers. The case n = 1 was known before ([12]); the rationality of λls is used to establish the theorem for the “joint” case n ≥ 2. As a corollary, the joint functional independence for those functions is shown.

scholarly journals A MIXED JOINT UNIVERSALITY THEOREM FOR ZETA-FUNCTIONS. II

2014 ◽  
Vol 19 (1) ◽  
pp. 52-65 ◽  
Author(s):  
Vaida Pocevičienė ◽  
Darius Šiaučiūnas
Keyword(s):  
Zeta Function ◽  
Cusp Form ◽  
Analytic Functions ◽  
Zeta Functions ◽  
Joint Universality ◽  
Universality Theorem ◽  
Joint Universality Theorem ◽  
Independent Parameters

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.

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.

The Joint Universality for L-Functions of Elliptic Curves

2004 ◽  
Vol 9 (4) ◽  
pp. 331-348
Author(s):  
V. Garbaliauskienė
Keyword(s):  
Elliptic Curves ◽  
Rational Numbers ◽  
Joint Universality ◽  
Universality Theorem ◽  
Joint Universality Theorem

A joint universality theorem in the Voronin sense for L-functions of elliptic curves over the field of rational numbers is proved.

The joint universality for periodic Hurwitz zeta-functions

Analysis ◽  
2006 ◽  
Vol 26 (3) ◽  
Author(s):  
Antanas Laurinčikas
Keyword(s):  
Zeta Functions ◽  
Periodic Coefficients ◽  
Joint Universality ◽  
Universality Theorem ◽  
Joint Universality Theorem

We prove a joint universality theorem for the Hurwitz zeta-functions with periodic coefficients.

scholarly journals A WEIGHTED VERSION OF THE MISHOU THEOREM

2021 ◽  
Vol 26 (1) ◽  
pp. 21-33
Author(s):  
Antanas Laurinčikas ◽  
Darius Šiaučiūnas ◽  
Gediminas Vadeikis
Keyword(s):  
Analytic Functions ◽  
Zeta Functions ◽  
Positive Density ◽  
Weighted Version ◽  
Joint Universality ◽  
Universality Theorem ◽  
Joint Universality Theorem

In 2007, H. Mishou obtained a joint universality theorem for the Riemann and Hurwitz zeta-functions ζ(s) and ζ(s,α) with transcendental parameter α on the approximation of a pair of analytic functions by shifts (ζ(s+iτ),ζ(s+iτ,α)), τ R. In the paper, the Mishou theorem is generalized for the set of above shifts having a weighted positive lower density. Also, the case of a positive density is considered.

scholarly journals A JOINT UNIVERSALITY THEOREM FOR PERIODIC HURWITZ ZETA-FUNCTIONS

2008 ◽  
Vol 78 (1) ◽  
pp. 13-33 ◽  
Author(s):  
A. JAVTOKAS ◽  
A. LAURINČIKAS
Keyword(s):  
Zeta Functions ◽  
Joint Universality ◽  
Universality Theorem ◽  
Joint Universality Theorem

AbstractWe prove a joint universality theorem in the Voronin sense for the periodic Hurwitz zeta-functions.

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.

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