An explicit form of limit distribution with weight for the Lerch zeta-function in the space of analytic functions

1997 ◽  
Vol 37 (3) ◽  
pp. 230-242 ◽  
Author(s):  
R. Garunkštis
Keyword(s):  
Zeta Function ◽  
Explicit Form ◽  
Limit Distribution ◽  
Analytic Functions ◽  
Space Of Analytic Functions ◽  
Lerch 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.

scholarly journals ON DISCRETE UNIVERSALITY OF COMPOSITE FUNCTIONS

2012 ◽  
Vol 17 (2) ◽  
pp. 271-280 ◽  
Author(s):  
Jovita Rašytė
Keyword(s):  
Analytic Function ◽  
Zeta Function ◽  
Riemann Zeta Function ◽  
Analytic Functions ◽  
Space Of Analytic Functions ◽  
Composite Functions ◽  
The Riemann Zeta Function ◽  
Fixed Positive Number ◽  
Riemann Zeta ◽  
Discrete Universality

In 1975, S.M. Voronin proved that the Riemann zeta-function ζ (s) is universal in the sense that its shifts approximate uniformly on some sets any analytic function. Let h be a fixed positive number such that exp is irrational for all . In the paper, the classes of functions F such that the shifts F (ζ (s + imh)), , approximate any analytic function are presented. For the proof of theorems, some elements of the space of analytic functions are applied.

HANKEL DETERMINANT FOR CERTAIN SUBCLASS OF ANALYTIC FUNCTIONS ASSOIATED WITH GENERALIZED SRIVASTAVA–ATTIYA OPERATOR

2020 ◽  
Vol 3 (1) ◽  
pp. 1-9
Author(s):  
Somaya Mohammed Alkabaily ◽  
Nagat Muftah Alabbar
Keyword(s):  
Zeta Function ◽  
Upper Bound ◽  
Analytic Functions ◽  
Hankel Determinant ◽  
Lerch Zeta Function ◽  
Second Hankel Determinant

This paper is to introduce a certain class of analytic functions denoted by  which is defined by generalized Srivastava – Attiya operator. This operator is associated with Hurwitz-Lerch Zeta function, obtain an upper bound to the second Hankel determinant  for  the class .

ON THE UNIVERSALITY OF THE HURWITZ ZETA-FUNCTION

2012 ◽  
Vol 09 (01) ◽  
pp. 155-165 ◽  
Author(s):  
ANTANAS LAURINČIKAS
Keyword(s):  
Analytic Function ◽  
Uniform Convergence ◽  
Zeta Function ◽  
Analytic Functions ◽  
Hurwitz Zeta Function ◽  
Space Of Analytic Functions ◽  
Rational Parameter ◽  
Compact Subsets

It is known that the Hurwitz zeta-function ζ(s, α) with transcendental or rational parameter α is universal in the sense that its shifts ζ(s + iτ, α), τ ∈ ℝ, approximate with a given accuracy any analytic function uniformly on compact subsets of the strip D = {s ∈ ℂ : ½ < σ < 1}. Let H(D) denote the space of analytic functions on D equipped with the topology of uniform convergence on compacta. In the paper, the classes of functions F : H(D) → H(D) such that F(ζ(s, α)) is universal in the above sense are considered. For example, if F is continuous and, for each polynomial p = p(s), the set F-1{p} is non-empty, then F(ζ(s, α)) with transcendental α is universal.

scholarly journals A Two-Dimentional Discrete Limit Theorem in the Space of Analytic Functions for Mellin Transforms of the Riemann Zeta-Function

2008 ◽  
Vol 13 (2) ◽  
pp. 159-167 ◽  
Author(s):  
V. Balinskaitė ◽  
V. Laurinčikas
Keyword(s):  
Limit Theorem ◽  
Zeta Function ◽  
Riemann Zeta Function ◽  
Analytic Functions ◽  
Critical Line ◽  
Space Of Analytic Functions ◽  
Mellin Transforms ◽  
Convergence Of Probability Measures ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

In the paper, a two-dimentional discrete limit theorem in the sense of weak convergence of probability measures in the space of analytic functions for Mellin transforms of the Riemann zeta-function on the critical line is obtained.

Sign in / Sign up

Export Citation Format

Share Document