Results 1 to 10 of about 47 (31)

On Universality of Some Beurling Zeta-Functions

Axioms
Let P be the set of generalized prime numbers, and ζP(s), s=σ+it, denote the Beurling zeta-function associated with P. In the paper, we consider the approximation of analytic functions by using shifts ζP(s+iτ), τ∈R. We assume the classical axioms for the
Andrius Geštautas, Antanas Laurinčikas
doaj   +5 more sources

On Value Distribution of Certain Beurling Zeta-Functions

Mathematics
In this paper, the approximation of analytic functions by shifts ζP(s+iτ) of Beurling zeta-functions ζP(s) of certain systems P of generalized prime numbers is discussed. It is required that the system of generalized integers NP generated by P satisfies ∑
Antanas Laurinčikas
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On Discrete Shifts of Some Beurling Zeta Functions

Mathematics
We consider the Beurling zeta function ζP(s), s=σ+it, of the system of generalized prime numbers P with generalized integers m satisfying the condition ∑m⩽x1=ax+O(xδ), a>0, 0⩽δσP with some σP0, there exists a closed non-empty set of analytic functions ...
Antanas Laurinčikas, Darius Šiaučiūnas   +1 more
doaj   +5 more sources

On probabilistic generalizations of the Nyman-Beurling criterion for the zeta function [PDF]

Confluentes Mathematici, 2021
The Nyman-Beurling criterion is an approximation problem in the space of square integrable functions on ( 0 , ∞ )
Hillion, Erwan, Darses, Sébastien
exaly   +3 more sources

On Functional Independence of Beurling Zeta-Functions

Axioms
Let P be a system of generalized prime numbers, and NP the corresponding system of generalized integers.
Antanas Laurinčikas, Darius Šiaučiūnas   +1 more
doaj   +3 more sources

Beurling Zeta Functions, Generalised Primes, and Fractal Membranes [PDF]

Acta Applicandae Mathematicae, 2006
We study generalised prime systems $\mathcal{P ...
Michel L Lapidus
exaly   +4 more sources

On Joint Approximation of Analytic Functions by Beurling Zeta-Functions

Mathematics
For j=1,…,r, let Pj be a system of generalized prime numbers, NPj the corresponding system of generalized integers, and ζPj(s), s=σ+it, the Beurling zeta-function. In the paper, we consider simultaneous approximation of a collection of analytic functions
Andrius Geštautas, Antanas Laurinčikas, Darius Šiaučiūnas   +2 more
doaj   +2 more sources

New zero-density estimates for the Beurling zeta function

Acta Arithmetica
In two previous papers the second author proved some Carlson type density theorems for zeroes in the critical strip for Beurling zeta functions satisfying Axiom A of Knopfmacher. In the first of these invoking two additonal conditions were needed, while in the second an explicit, fully general result was obtained.
Szilárd RÉVÉSZ, János Pintz
exaly   +3 more sources

Distribution of Beurling primes and zeroes of the Beurling zeta function I. Distribution of the zeroes of the zeta function of Beurling

Mathematika, 2020
We prove three results on the density resp. local density and clustering of zeros of the Beurling zeta function $ζ(s)$ close to the one-line $σ:=\Re s=1$. The analysis here brings about some news, sometimes even for the classical case of the Riemann zeta function.
openaire   +5 more sources

Ω-results for Beurling's zeta function and lower bounds for the generalised Dirichlet divisor problem [PDF]

Journal of Number Theory, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources