A survey of the theory of mixed joint universality for zeta-functions

2021 ◽  
pp. 47-60
Author(s):  
Roma Kačinskaitė ◽  
Kohji Matsumoto
Keyword(s):  
Zeta Functions ◽  
Joint Universality

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.

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 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 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 JOINT UNIVERSALITY OF DIRICHLET L-FUNCTIONS AND PERIODIC HURWITZ ZETA-FUNCTIONS

2012 ◽  
Vol 17 (5) ◽  
pp. 673-685 ◽  
Author(s):  
Kęstutis Janulis ◽  
Antanas Laurinčikas ◽  
Renata Macaitienė ◽  
Darius Šiaučiūnas
Keyword(s):  
Analytic Functions ◽  
Zeta Functions ◽  
Rational Numbers ◽  
Joint Universality ◽  
Compact Subsets

In the paper, we prove that every system of analytic functions can be approximated simultaneously uniformly on compact subsets of some region by a collection consisting of shifts of Dirichlet L-functions with pairwise non-equivalent characters and periodic Hurwitz zeta-functions with parameters algebraically independent over the field of rational numbers.

The mixed joint universality for a class of zeta-functions

2015 ◽  
Vol 288 (16) ◽  
pp. 1900-1909 ◽  
Author(s):  
Roma Kačinskaitė ◽  
Kohji Matsumoto
Keyword(s):  
Zeta Functions ◽  
Joint Universality
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