Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3279
Abstract
In the paper, a theorem on approximation of a wide class of analytic functions by generalized shifts $\zeta_{u_T}(s+i\varphi(\tau))$ of an absolutely convergent Dirichlet series $\zeta_{u_T}(s)$ which in the mean is close to the Riemann zeta-function is obtained. Here $\varphi(\tau)$ is a monotonically increasing differentiable function having a monotonic continuous derivative such that $\varphi(2\tau)\max\limits_{\tau\leqslant t\leqslant 2\tau} \frac{1}{\varphi'(t)} \ll \tau$ as $\tau\to\infty$, and $u_T\to\infty$ and $u_T\ll T^2$ as $T\to\infty$.
Keywords
Haar measure, Mergelyan theorem, Riemann zeta-function, universality, weak convergence
First Page
2440
Last Page
2449
Recommended Citation
LAURINCIKAS, ANTANAS; MACAITIENE, RENATA; and SIAUCIUNAS, DARIUS
(2022)
"Universality of an absolutely convergent Dirichlet series with modified shifts,"
Turkish Journal of Mathematics: Vol. 46:
No.
6, Article 27.
https://doi.org/10.55730/1300-0098.3279
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss6/27