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 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 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.

scholarly journals A joint limit theorem for zeta-functions of newforms

2012 ◽  
Vol 53 ◽  
Author(s):  
Gintautas Misevičius
Keyword(s):  
Limit Theorem ◽  
Complex Plane ◽  
Zeta Functions ◽  
Joint Limit Theorem ◽  
Joint Limit

In the paper a joint limit theorem for zeta-functions of newforms on the complex plane 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 joint limit theorem for compactly regenerative ergodic transformations

2011 ◽  
Vol 203 (1) ◽  
pp. 33-45 ◽  
Author(s):  
David Kocheim ◽  
Roland Zweimüller
Keyword(s):  
Limit Theorem ◽  
Ergodic Transformations ◽  
Joint Limit Theorem ◽  
Joint Limit

scholarly journals Central limit theorem for linear processes generated by IID random variables under the sub-linear expectation

2021 ◽  
Vol 36 (2) ◽  
pp. 243-255
Author(s):  
Wei Liu ◽  
Yong Zhang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Invariance Principle ◽  
Random Variables ◽  
Probability Measures ◽  
Linear Processes ◽  
The Central Limit Theorem

AbstractIn this paper, we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng [19]. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov’s central limit theorem and invariance principle to the case where probability measures are no longer additive.

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 AN INDICATOR FUNCTION LIMIT THEOREM IN DYNAMICAL SYSTEMS

2011 ◽  
Vol 11 (04) ◽  
pp. 681-690
Author(s):  
OLIVIER DURIEU ◽  
DALIBOR VOLNÝ
Keyword(s):  
Dynamical System ◽  
Limit Theorem ◽  
Dynamical Systems ◽  
Indicator Function ◽  
Constructive Proof ◽  
Probability Measures

We give a constructive proof of the following result: in all aperiodic dynamical system, for all sequences (an)n∈ℕ ⊂ ℝ+ such that an ↗ ∞ and [Formula: see text] as n → ∞, there exists a set [Formula: see text] having the property that the sequence of the distributions of [Formula: see text] is dense in the space of all probability measures on ℝ. This extends a result of O. Durieu and D. Volný, Ergod. Th. Dynam. Syst. to the non-ergodic case.

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