| Title |
On discrete shifts of some Beurling zeta functions / |
| Authors |
LaurinΔikas, Antanas ; Ε iauΔiΕ«nas, Darius |
| DOI |
10.3390/math13010048 |
| Full Text |
|
| Is Part of |
Mathematics.. Basel : MDPI. 2025, vol. 13, iss. 1, art. no. 48, p. [1-17].. eISSN 2227-7390 |
| Keywords [eng] |
approximation of analytic functions ; Beurling zeta function ; generalized integers ; generalized primes ; Haar measure ; random element ; weak convergence |
| Abstract [eng] |
We consider the Beurling zeta function πβ(π ), π =π+ππ‘, of the system of generalized prime numbers β with generalized integers m satisfying the condition βπβ©½π₯1=ππ₯+π(π₯πΏ), π>0, 0β©½πΏ<1, and suppose that πβ(π ) has a bounded mean square for π>πβ with some πβ<1. Then, we prove that, for every β>0, there exists a closed non-empty set of analytic functions that are approximated by discrete shifts πβ(π +ππβ). This set shifts has a positive density. For the proof, a weak convergence of probability measures in the space of analytic functions is applied. |
| Published |
Basel : MDPI |
| Type |
Journal article |
| Language |
English |
| Publication date |
2025 |
| CC license |
|
