Results 1 to 10 of about 32,945 (273)

On the Mishou Theorem for Zeta-Functions with Periodic Coefficients

Mathematics, 2023
Let a={am} and b={bm} be two periodic sequences of complex numbers, and, additionally, a is multiplicative. In this paper, the joint approximation of a pair of analytic functions by shifts (ζnT(s+iτ;a),ζnT(s+iτ,α;b)) of absolutely convergent Dirichlet ...
Aidas Balčiūnas, Mindaugas Jasas, Renata Macaitienė, Darius Šiaučiūnas   +3 more
doaj   +5 more sources

On the Zeta Function of a Periodic-Finite-Type Shift [PDF]

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2013
Periodic-finite-type shifts (PFT's) are sofic shifts which forbid the appearance of finitely many pre-specified words in a periodic manner. The class of PFT's strictly includes the class of shifts of finite type (SFT's). The zeta function of a PET is a generating function for the number of periodic sequences in the shift.
Akiko Manada, Navin Kashyap
exaly   +5 more sources

A Weighted Universality Theorem for Periodic Zeta-Functions

Mathematical Modelling and Analysis, 2017
The periodic zeta-function ζ(s; a), s = σ + it is defined for σ > 1 by the Dirichlet series with periodic coefficients and is meromorphically continued to the whole complex plane.
Renata Macaitienė, Mindaugas Stoncelis, Darius Šiaučiūnas   +2 more
doaj   +5 more sources

On shifts of periodic zeta-function in short intervals

Mathematical Modelling and Analysis
The periodic zeta-function $\zeta(s; a)$, $s = \sigma + it$, $a = \{a_m \in \mathbb{C} : m \in \mathbb{N}\}$, in the half-plane $\sigma > 1$ is defined by Dirichlet series with periodic coefficients $a_m$, and has the meromorphic continuation to the ...
Marius Grigaliūnas, Antanas Laurinčikas, Darius Šiaučiūnas   +2 more
doaj   +5 more sources

Orbit Growth of Periodic-Finite-Type Shifts via Artin–Mazur Zeta Function

Mathematics, 2020
The prime orbit and Mertens’ orbit counting functions describe the growth of closed orbits in a discrete dynamical system in a certain way. In this paper, we prove the asymptotic behavior of these functions for a periodic-finite-type shift.
Azmeer Nordin, Mohd Salmi Md Noorani
doaj   +4 more sources

The zeta function of a periodic-finite-type shift [PDF]

2009 IEEE International Symposium on Information Theory, 2009
The class of periodic-finite-type shifts (PFT's) is a class of sofic shifts that strictly includes the class of shifts of finite type (SFT's), and the zeta function of a PFT is a generating function for the number of periodic sequences in the shift. In this paper, we derive a useful formula for the zeta function of a PFT.
Akiko Manada, Navin Kashyap
exaly   +3 more sources

On the fourth moment of the periodic zeta-function

Lietuvos Matematikos Rinkinys, 2004
There is not abstract.
Darius Šiaučiūnas, Algimantas Laurutis   +1 more
doaj   +4 more sources

On the mean square of the periodic zeta-function

Lietuvos Matematikos Rinkinys, 2003
There is not abstract.
Audrius Kačėnas, Darius Šiaučiūnas
doaj   +5 more sources

On the periodic zeta-function with rational parameter

Lietuvos Matematikos Rinkinys, 2011
We obtain an asymptotic formula with estimated error term for the fourth power moment of the periodic zeta-function with rational parameter.
Sondra Černigova
doaj   +3 more sources

Sum of the periodic zeta-function over the nontrivial zeros of the Riemann zeta-function [PDF]

Analysis (Germany), 2008
The periodic zeta-function in the title is the analytic continuation into the entire \(s\)-plane of the Dirichlet series \[ L(s,k/l)= \sum^\infty_{n=1} e^{2\pi ink/l} n^{-s}, \] where \(k\) and \(l\) are coprime positive integers with \(k< l\). If \(\rho= \beta+ i\gamma\) denotes a typical nontrivial zero of the Riemann zeta function, \textit{J ...
Ramunas Garunkštis, Justas Kalpokas
exaly   +3 more sources