| Title |
Approximation of analytic functions by discrete shifts of the Hurwitz zeta-function in short intervals |
| Authors |
Laurinčikas, Antanas ; Šiaučiūnas, Darius |
| DOI |
10.1515/ms-2026-0287 |
| Full Text |
|
| Is Part of |
Mathematica Slovaca.. Berlin : De Gruyter. 2026, vol. 76, iss. 3, p. 679-695.. ISSN 0139-9918. eISSN 1337-2211 |
| Keywords [eng] |
approximation of analytic functions ; Hurwitz zeta-function ; universality ; weak convergence |
| Abstract [eng] |
In the paper, we prove theorems in short intervals on approximation of analytic functions by shifts (Formula presented), of the Hurwitz zeta-function. Two cases are discussed. In the first case, it is assumed that the set (Formula presented) is linearly independent over Q, and it is obtained that the set of the above shifts approximating every analytic function defined on the strip (Formula presented) has a positive lower density (or density) in the interval of length H, (Formula presented). The second case is devoted to arbitrary 0 < α < 1, α ≠ 1/2. It is obtained that there exists a closed non-empty set (Formula presented) of analytic functions defined on D such that, for every (Formula presented), the set of shifts ζ(s + ikh, α) approximating the function f also has a positive lower density (or density) in the above interval. These results extend the known theorems proved for the interval of length N. |
| Published |
Berlin : De Gruyter |
| Type |
Journal article |
| Language |
English |
| Publication date |
2026 |
| CC license |
|
