Joint discrete universality for periodic zeta-functions. III

2020 ◽  
pp. 1-15
Author(s):  
Antanas Laurinčikas
Keyword(s):  
Zeta Functions ◽  
Discrete Universality

scholarly journals On joint approximation of analytic functions by nonlinear shifts of zeta-functions of certain cusp forms

2020 ◽  
Vol 25 (1) ◽  
Author(s):  
Antanas Laurinčikas ◽  
Darius Šiaučiūnas ◽  
Adelė Vaiginytė
Keyword(s):  
Analytic Functions ◽  
Simultaneous Approximation ◽  
Zeta Functions ◽  
Growth Conditions ◽  
Cusp Forms ◽  
Differentiable Functions ◽  
Joint Approximation ◽  
Discrete Universality ◽  
Positive Integers

In the paper, joint discrete universality theorems on the simultaneous approximation of a collection of analytic functions by a collection of discrete shifts of zeta-functions attached to normalized Hecke-eigen cusp forms are obtained. These shifts are defined by means of nonlinear differentiable functions that satisfy certain growth conditions, and their combination on positive integers is uniformly distributed modulo 1.

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: A FURTHER GENERALIZATION

2020 ◽  
Vol 25 (4) ◽  
pp. 569-583
Author(s):  
Roma Kačinskaitė ◽  
Kohji Matsumoto
Keyword(s):  
Linear Independence ◽  
Zeta Functions ◽  
Prime Numbers ◽  
Value Distribution ◽  
Arithmetic Progressions ◽  
Independence Condition ◽  
Discrete Universality

We present the most general at this moment results on the discrete mixed joint value-distribution (Theorems 5 and 6) and the universality property (Theorems 3 and 4) for the class of Matsumoto zeta-functions and periodic Hurwitz zeta-functions under certain linear independence condition on the relevant parameters, such as common differences of arithmetic progressions, prime numbers etc.

scholarly journals Joint universality of periodic zeta-functions with multiplicative coefficients. II

2021 ◽  
Vol 26 (3) ◽  
pp. 550-564
Author(s):  
Antanas Laurinčikas ◽  
Darius Šiaučiūnas ◽  
Monika Tekorė
Keyword(s):  
Analytic Functions ◽  
Pair Correlation ◽  
Zeta Functions ◽  
Weak Form ◽  
Joint Universality ◽  
Nontrivial Zeros ◽  
Nonlinear Anal ◽  
Model Control ◽  
Riemann Zeta ◽  
Discrete Universality

In the paper, a joint discrete universality theorem for periodic zeta-functions with multiplicative coefficients on the approximation of analytic functions by shifts involving the sequence f kg of imaginary parts of nontrivial zeros of the Riemann zeta-function is obtained. For its proof, a weak form of the Montgomery pair correlation conjecture is used. The paper is a continuation of [A. Laurinčikas, M. Tekorė, Joint universality of periodic zeta-functions with multiplicative coefficients, Nonlinear Anal. Model. Control, 25(5):860–883, 2020] using nonlinear shifts for approximation of analytic functions.

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