| Title |
Joint approximation of analytic functions by the shifts of Hurwitz zeta-functions in short intervals |
| Authors |
Laurinčikas, Antanas ; Šiaučiūnas, Darius |
| DOI |
10.1515/math-2025-0173 |
| Full Text |
|
| Is Part of |
Open mathematics.. Warsaw : De Gruyter Open Access. 2025, vol. 23, art. no. 20250173, p. [1-12].. eISSN 2391-5455 |
| Keywords [eng] |
Hurwitz zeta-function ; joint universality ; space of analytic functions ; weak convergence of probability measures |
| Abstract [eng] |
In the paper, we obtain that, for algebraically independent over $\QQ$ parameters $\alpha_1, \dots, \alpha_r$, there are infinitely many shifts $(\zeta(s+i\tau, \alpha_1), \dots, \zeta(s+i\tau, \alpha_r))$ of Hurwitz zeta-functions with $\tau\in[T, T+H]$, $T^{27/82}\leqslant H\leqslant T^{1/2}$, that approximate any $r$-tuple of analytic {functions on the strip $\{s\in \CC: 1/2< \sigma<1\}$.} More precisely, the latter set of shifts has a positive density. For the proof, a probabilistic approach is applied. |
| Published |
Warsaw : De Gruyter Open Access |
| Type |
Journal article |
| Language |
English |
| Publication date |
2025 |
| CC license |
|
