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Gram Points in the Universality of the Dirichlet Series with Periodic Coefficients.
- Source :
-
Mathematics (2227-7390) . Nov2023, Vol. 11 Issue 22, p4615. 14p. - Publication Year :
- 2023
-
Abstract
- Let a = { a m : m ∈ N } be a periodic multiplicative sequence of complex numbers and L (s ; a) , s = σ + i t a Dirichlet series with coefficients a m . 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 + i h t k ; a) , h > 0 , k ∈ N , where { t k : 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 11
- Issue :
- 22
- Database :
- Academic Search Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 173862810
- Full Text :
- https://doi.org/10.3390/math11224615