scholarly journals A general joint discrete universality theorem for Hurwitz zeta-functions

2015 ◽  
Vol 154 ◽  
pp. 44-62 ◽  
Author(s):  
Antanas Laurinčikas
Keyword(s):  
Zeta Functions ◽  
Universality Theorem ◽  
Discrete Universality

scholarly journals Extension of the discrete universality theorem for zeta-functions of certain cusp forms

2018 ◽  
Vol 23 (6) ◽  
pp. 961-973
Author(s):  
Antanas Laurinčikas ◽  
Darius Šiaučiūnas ◽  
Adelė Vaiginytė
Keyword(s):  
Analytic Functions ◽  
Zeta Functions ◽  
Growth Conditions ◽  
Cusp Forms ◽  
Continuous Derivative ◽  
Natural Growth ◽  
Universality Theorem ◽  
Discrete Universality ◽  
Positive Integers

In the paper, an universality theorem on the approximation of analytic functions by generalized discrete shifts of zeta functions of Hecke-eigen cusp forms is obtained. These shifts are defined by using the function having continuous derivative satisfying certain natural growth conditions and, on positive integers, uniformly distributed modulo 1.

scholarly journals A WEIGHTED DISCRETE UNIVERSALITY THEOREM FOR PERIODIC ZETA-FUNCTIONS. II

2017 ◽  
Vol 22 (6) ◽  
pp. 750-762 ◽  
Author(s):  
Renata Macaitienė ◽  
Mindaugas Stoncelis ◽  
Darius Šiaučiūnas
Keyword(s):  
Zeta Function ◽  
Wide Class ◽  
Analytic Functions ◽  
Zeta Functions ◽  
Periodic Sequence ◽  
Universality Theorem ◽  
Discrete Universality

In the paper, a weighted theorem on the approximation of a wide class of analytic functions by shifts ζ(s + ikαh; a), k ∈ N, 0 < α < 1, and h > 0, of the periodic zeta-function ζ(s; a) with multiplicative periodic sequence a, is obtained.

scholarly journals On mixed joint discrete universality for a class of zeta-functions. II

2019 ◽  
Vol 59 (1) ◽  
pp. 54-66
Author(s):  
Roma Kačinskaitė ◽  
Kohji Matsumoto
Keyword(s):  
Zeta Functions ◽  
Discrete 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.

A discrete universality theorem for general Dirichlet series

Analysis ◽  
2006 ◽  
Vol 26 (3) ◽  
Author(s):  
Renata Macaitiene
Keyword(s):  
Dirichlet Series ◽  
General Dirichlet Series ◽  
Universality Theorem ◽  
Discrete Universality

We prove a discrete universality theorem for functions given by general Dirichlet series, satisfying several conditions.

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.

Sign in / Sign up

Export Citation Format

Share Document