scholarly journals A Joint Limit Theorem for Laplace Transforms of the Riemann Zeta–Function

2007 ◽  
Vol 12 (4) ◽  
pp. 503-510
Author(s):  
A. Laurinčikas
Keyword(s):  
Limit Theorem ◽  
Weak Convergence ◽  
Laplace Transforms ◽  
Probability Measures ◽  
Convergence Of Probability Measures ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Joint Limit Theorem ◽  
Riemann Zetafunction ◽  
Joint Limit

In the paper, a joint limit theorem in the sense of weak convergence of probability measures on the complex plane for Laplace transforms of the Riemann zetafunction is obtained.

scholarly journals The joint distribution of the Riemann zeta - function

2006 ◽  
Vol 73 (2) ◽  
pp. 201-217 ◽  
Author(s):  
A. Laurinčikas
Keyword(s):  
Weak Convergence ◽  
Zeta Function ◽  
Asymptotic Distribution ◽  
Riemann Zeta Function ◽  
Joint Distribution ◽  
Probability Measures ◽  
Convergence Of Probability Measures ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

In the paper the asymptotic distribution of (|ζ(s)|,ζ(s)), where ζ(s) is the Riemann zeta - function, in the sense of weak convergence of probability measures is considered. For this, the continuity theorems for probability measures on ℝ × ℂ are used. Some aspects of the dependence of |ζ(s)| and ζ(s) are also discussed.

scholarly journals Value-distribution of twisted L-functions of normalized cusp forms

2010 ◽  
Vol 51 ◽  
Author(s):  
Alesia Kolupayeva
Keyword(s):  
Limit Theorem ◽  
Weak Convergence ◽  
Complex Plane ◽  
Dirichlet Character ◽  
Value Distribution ◽  
Cusp Forms ◽  
Probability Measures ◽  
Convergence Of Probability Measures

A limit theorem in the sense of weak convergence of probability measures on the complex plane for twisted with Dirichlet character L-functions of holomorphic normalized Hecke eigen cusp forms with an increasing modulus of the character is proved.

On Joint Distribution of General Dirichlet Series

2003 ◽  
Vol 8 (2) ◽  
pp. 27-39 ◽  
Author(s):  
J. Genys ◽  
A. Laurinčikas
Keyword(s):  
Limit Theorem ◽  
Weak Convergence ◽  
Dirichlet Series ◽  
Joint Distribution ◽  
Meromorphic Functions ◽  
General Dirichlet Series ◽  
Joint Limit Theorem ◽  
Space Of Meromorphic Functions ◽  
Weaker Conditions ◽  
Joint Limit

In the paper a joint limit theorem in the sense of the weak convergence in the space of meromorphic functions for general Dirichlet series is proved under weaker conditions as in [1].

A Discrete Limit Theorem for L-Functions of Elliptic Curves

2018 ◽  
Vol 48 (2) ◽  
pp. 27-29
Author(s):  
Virginija Garbaliauskienė ◽  
Antanas Garbaliauskas
Keyword(s):  
Limit Theorem ◽  
Probability Measure ◽  
Weak Convergence ◽  
Real Number ◽  
Elliptic Curves ◽  
Irrational Number ◽  
Probability Measures ◽  
Convergence Of Probability Measures ◽  
Main Statement

In the paper, we prove the discrete limit theorem in the sense of the weak convergence of probability measures in the space of analytic on DV = {s ∈ C : 1 < σ < 3/2, |t| <  V} functions for L-functions of elliptic curves LE(s). The main statement of the paper is as follows. Let h > 0 be a fixed real number such that exp {2πk/h} is an irrational number for all k∈Z\{0}. Then the probability measure μN(LE(s + imh)∈A), A ∈ B(H(DV)), converges weakly to the measure PLE as N→∞.

A Weighted Universality Theorem for L-Functions of Elliptic Curves

2018 ◽  
Vol 48 (2) ◽  
pp. 18-21
Author(s):  
Antanas Garbaliauskas ◽  
Virginija Garbaliauskienė
Keyword(s):  
Limit Theorem ◽  
Weak Convergence ◽  
Elliptic Curves ◽  
Analytic Functions ◽  
Rational Numbers ◽  
Probability Measures ◽  
Space Of Analytic Functions ◽  
Continuous Type ◽  
Universality Theorem ◽  
Convergence Of Probability Measures

In the paper, a short survey on universality results for L-functions of elliptic curves over the field of rational numbers is given and weighted universality theorem is proven. All stated universality theorems are of continuous type. The proof of the universality for L-functions of elliptic curves is based on a limit theorem in the sense of weak convergence of probability measures in the space of analytic functions.

scholarly journals A discrete limit theorem for the periodic Hurwitz zeta-function. II

2016 ◽  
Vol 57 ◽  
Author(s):  
Audronė Rimkevičienė
Keyword(s):  
Limit Theorem ◽  
Weak Convergence ◽  
Zeta Function ◽  
Complex Plane ◽  
Hurwitz Zeta Function ◽  
Probability Measures ◽  
Convergence Of Probability Measures ◽  
Discrete Type

In the paper, we prove a limit theorem of discrete type on the weak convergence of probability measures on the complex plane for the periodic Hurwitz zeta-function.

Value Distribution of General Dirichlet series. VI

2005 ◽  
Vol 10 (3) ◽  
pp. 235-246
Author(s):  
A. Laurinčikas
Keyword(s):  
Limit Theorem ◽  
Weak Convergence ◽  
Dirichlet Series ◽  
Complex Plane ◽  
Value Distribution ◽  
Probability Measures ◽  
General Dirichlet Series ◽  
New Class ◽  
Convergence Of Probability Measures

In the paper a limit theorem in the sense of weak convergence of probability measures on the complex plane for a new class of general Dirichlet series is obtained.

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.

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