On Discrete Approximation of Analytic Functions by Shifts of the Lerch Zeta Function

Audronė Rimkevičienė and Darius Šiaučiūnas ()
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Audronė Rimkevičienė: Faculty of Business and Technologies, Šiauliai State University of Applied Sciences, Aušros av. 40, LT-76241 Šiauliai, Lithuania
Darius Šiaučiūnas: Institute of Regional Development, Šiauliai Academy, Vilnius University, P. Višinskio Str. 25, LT-76351 Šiauliai, Lithuania

Mathematics, 2022, vol. 10, issue 24, 1-13

Abstract: The Lerch zeta function is defined by a Dirichlet series depending on two fixed parameters. In the paper, we consider the approximation of analytic functions by discrete shifts of the Lerch zeta function, and we prove that, for arbitrary parameters and a step of arithmetic progression, there is a closed non-empty subset of the space of analytic functions defined in the critical strip such that its functions can be approximated by discrete shifts of the Lerch zeta function. The set of those shifts is infinite, and it has a positive density. For the proof, the weak convergence of probability measures in the space of analytic functions is applied.

Keywords: approximation of analytic functions; Hurwitz zeta function; Lerch zeta function; weak convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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