On Value Distribution of Certain Beurling Zeta-Functions

Antanas Laurinčikas ()
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Antanas Laurinčikas: Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko str. 24, LT-03225 Vilnius, Lithuania

Mathematics, 2024, vol. 12, issue 3, 1-15

Abstract: In this paper, the approximation of analytic functions by shifts ζ P ( s + i τ ) of Beurling zeta-functions ζ P ( s ) of certain systems P of generalized prime numbers is discussed. It is required that the system of generalized integers N P generated by P satisfies ∑ m ⩽ x , m ∈ N 1 = a x + O ( x δ ) , a > 0 , 0 ⩽ δ < 1 , and the function ζ P ( s ) in some strip lying in σ ^ < σ < 1 , σ ^ > δ , which has a bounded mean square. Proofs are based on the convergence of probability measures in some spaces.

Keywords: Beurling zeta-function; generalized integers; generalized prime numbers; weak convergence of probability measures (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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