scholarly journals A JOINT ELLIOTT TYPE THEOREM FOR TWISTS OF L-FUNCTIONS OF ELLIPTIC CURVES

2016 ◽  
Vol 21 (6) ◽  
pp. 752-761
Author(s):  
Virginija Garbaliauskienė ◽  
Antanas Laurinčikas
Keyword(s):  
Limit Theorem ◽  
Elliptic Curves ◽  
Analytic Functions ◽  
Type Theorem ◽  
Dirichlet Character ◽  
Probability Measures ◽  
Space Of Analytic Functions ◽  
Limit Measure ◽  
Joint Limit Theorem ◽  
Joint Limit

We consider a collection of L-functions of elliptic curves twisted by a Dirichlet character modulo q (q is a prime number), and prove for this collection a joint limit theorem for weakly convergent probability measures in the space of analytic functions as q → ∞. The limit measure is given explicitly.

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 LIMIT THEOREM FOR TWISTS OF L-FUNCTIONS OF ELLIPTIC CURVES

2014 ◽  
Vol 19 (5) ◽  
pp. 696-705 ◽  
Author(s):  
Virginija Garbaliauskienė ◽  
Antanas Laurinčikas
Keyword(s):  
Limit Theorem ◽  
Elliptic Curves ◽  
Complex Plane ◽  
Dirichlet Character ◽  
Probability Measures

In the paper, a limit theorem for weakly convergent probability measures on the complex plane for twisted with Dirichlet character L-functions of elliptic curves with an increasing modulus of the character is proved.

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 A JOINT LIMIT THEOREM FOR PERIODIC HURWITZ ZETA-FUNCTIONS WITH ALGEBRAIC IRRATIONAL PARAMETERS

2013 ◽  
Vol 18 (1) ◽  
pp. 149-159
Author(s):  
Danutė Genienė ◽  
Audronė Rimkevičienė
Keyword(s):  
Limit Theorem ◽  
Zeta Functions ◽  
Probability Measures ◽  
Joint Limit Theorem ◽  
Joint Limit

In the paper, a joint limit theorem for weakly convergent probability measures in ℂ r for periodic Hurwitz zeta-functions with algebraic irrational parameters satisfying certain independence conditions is obtained.

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.

scholarly journals LIMIT THEOREMS FOR TWISTS OF L-FUNCTIONS OF ELLIPTIC CURVES. II

2012 ◽  
Vol 17 (1) ◽  
pp. 90-99 ◽  
Author(s):  
Virginija Garbaliauskienė ◽  
Antanas Laurinčikas
Keyword(s):  
Limit Theorem ◽  
Elliptic Curves ◽  
Limit Theorems ◽  
Dirichlet Character

In the paper, a limit theorem for the argument of twisted with Dirichlet character L-functions of elliptic curves with an increasing modulus of the character is proved.

scholarly journals A Class of Integral Operators Preserving Subordination and Superordination for Analytic Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
H. A. Al-Kharsani ◽  
N. M. Al-Areefi ◽  
Janusz Sokół
Keyword(s):  
Hypergeometric Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Type Theorem ◽  
Integral Operators ◽  
Gauss Hypergeometric Function ◽  
Open Unit ◽  
Open Unit Disk ◽  
Space Of Analytic Functions ◽  
Sandwich Type

The purpose of the paper is to investigate several subordination- and superordination-preserving properties of a class of integral operators, which are defined on the space of analytic functions in the open unit disk. The sandwich-type theorem for these integral operators is also presented. Moreover, we consider an application of the subordination and superordination theorem to the Gauss hypergeometric function.

scholarly journals LIMIT THEOREMS FOR TWISTS OF L-FUNCTIONS OF ELLIPTIC CURVES. IV

2014 ◽  
Vol 19 (1) ◽  
pp. 66-74 ◽  
Author(s):  
Virginija Garbaliauskienė ◽  
Antanas Laurinčikas
Keyword(s):  
Limit Theorem ◽  
Elliptic Curves ◽  
Limit Theorems ◽  
Limit Measure

In this paper, we prove a multidimensional limit theorem for moduli of twists of L-functions of elliptic curves. The limit measure in this theorem is defined by the characteristic transforms.

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].

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