scholarly journals A weighted limit theorem for periodic Hurwitz zeta-function

2012 ◽  
Vol 53 ◽  
Author(s):  
Oleg Lukašonok
Keyword(s):  
Limit Theorem ◽  
Zeta Function ◽  
Complex Plane ◽  
Hurwitz Zeta Function ◽  
Probability Measures ◽  
Weighted Limit

In the paper, a weighted limit theorem for weakly convergent probability measures on the complex plane for the periodic Hurwitz zeta function is obtained.

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.

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

2015 ◽  
Vol 56 ◽  
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.

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 ON APPROXIMATION OF ANALYTIC FUNCTIONS BY PERIODIC HURWITZ ZETA-FUNCTIONS

2018 ◽  
Vol 24 (1) ◽  
pp. 20-33 ◽  
Author(s):  
Darius Siaučiūnas ◽  
Violeta Franckevič ◽  
Antanas Laurinčikas
Keyword(s):  
Zeta Function ◽  
Complex Plane ◽  
Analytic Functions ◽  
Zeta Functions ◽  
Periodic Sequence ◽  
Hurwitz Zeta Function ◽  
Complex Numbers ◽  
Closed Set

The periodic Hurwitz zeta-function ζ(s, α; a), s = σ +it, with parameter 0 < α ≤ 1 and periodic sequence of complex numbers a = {am } is defined, for σ > 1, by series sum from m=0 to ∞ am / (m+α)s, and can be continued moromorphically to the whole complex plane. It is known that the function ζ(s, α; a) with transcendental orrational α is universal, i.e., its shifts ζ(s + iτ, α; a) approximate all analytic functions defined in the strip D = { s ∈ C : 1/2 σ < 1. In the paper, it is proved that, for all 0 < α ≤ 1 and a, there exists a non-empty closed set Fα,a of analytic functions on D such that every function f ∈ Fα,a can be approximated by shifts ζ(s + iτ, α; a).

Application of the Hurwitz Zeta Function to the Evaluation of Certain Integrals

1993 ◽  
Vol 36 (3) ◽  
pp. 373-384 ◽  
Author(s):  
Zhang Nan Yue ◽  
Kenneth S. Williams
Keyword(s):  
Zeta Function ◽  
Complex Plane ◽  
Integral Representations ◽  
Simple Pole ◽  
Hurwitz Zeta Function ◽  
Improper Integrals

AbstractThe Hurwitz zeta function ζ(s, a) is defined by the seriesfor 0 < a ≤ 1 and σ = Re(s) > 1, and can be continued analytically to the whole complex plane except for a simple pole at s = 1 with residue 1. The integral functions C(s, a) and S(s, a) are defined in terms of the Hurwitz zeta function as follows:Using integral representations of C(s, a) and S(s, a), we evaluate explicitly a class of improper integrals. For example if 0 < a < 1 we show that

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.

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