Izvorni znanstveni članak

”Almost” universality of the Lerch zeta-function

Antanas Laurinčikas ; Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Vilnius, Lithuania

Sažetak

The Lerch zeta-function $L(\lambda ,\alpha ,s)$ with transcendental parameter $\alpha$, or with rational parameters $\alpha$ and $\lambda$ is universal, i.e., a wide class of analytic functions is approximated by shifts $L(\lambda ,\alpha ,s+i\tau )$, $\tau \in \mathbb{R}$. The case of algebraic irrational $\alpha$ is an open problem. In the paper, it is proved that, for all parameters $\alpha$, $0<\alpha <1$, and $\lambda$, $0<\lambda ⩽1$, including an algebraic irrational $\alpha$, there exists a closed non-empty set of analytic functions $F_{\alpha ,\lambda }$ such that every function $f\in F_{\alpha ,\lambda }$ can be approximated by shifts $L(\lambda ,\alpha ,s+i\tau )$.

Ključne riječi

Lerch zeta-function; support of probability measure; universality; weak convergence

Hrčak ID:

215154

URI

https://hrcak.srce.hr/215154

Datum izdavanja:

19.4.2019.

Posjeta: 931 *