| Title |
Gram points in the universality of the Dirichlet series with periodic coefficients |
| Authors |
Šiaučiūnas, Darius ; Tekorė, Monika |
| DOI |
10.3390/math11224615 |
| Full Text |
|
| Is Part of |
Mathematics: Special iss.: Analytic methods in number theory and allied fields.. Basel : MDPI. 2023, vol. 11, iss. 22, art. no. 4615, p. 1-14.. eISSN 2227-7390 |
| Keywords [eng] |
space of analytic functions ; approximation of analytic functions ; universality ; weak convergence |
| Abstract [eng] |
Let a = {am : m ∈ N} be a periodic multiplicative sequence of complex numbers and L(s; a), s = σ + it a Dirichlet series with coefficients am. In the paper, we obtain a theorem on the approximation of non-vanishing analytic functions defined in the strip 1 / 2 < σ < 1 via discrete shifts L(s + ihtk; a), h > 0, k ∈ N, where {tk : k ∈ N} is the sequence of Gram points. We prove that the set of such shifts approximating a given analytic function is infinite. This result extends and covers that of [Korolev, M.; Laurinčikas, A. A new application of the Gram points. Aequat. Math. 2019, 93, 859–873]. For the proof, a limit theorem on weakly convergent probability measures in the space of analytic functions is applied. |
| Published |
Basel : MDPI |
| Type |
Journal article |
| Language |
English |
| Publication date |
2023 |
| CC license |
|
