| Title | The approximation of analytic functions using shifts of the Lerch zeta-function in short intervals |
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| Authors | Laurinčikas, Antanas |
| DOI | 10.3390/axioms14060472 |
| Full Text |
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| Is Part of | Axioms.. Basel : MDPI. 2025, vol. 14, iss. 6, art. no. 472, p. [1-15].. ISSN 2075-1680 |
| Keywords [eng] | Hurwitz zeta-function ; Lerch zeta-function ; Mergelyan theorem ; short intervals ; universality ; weak convergence of probability measures |
| Abstract [eng] | In this paper, we obtain approximation theorems of classes of analytic functions by shifts L(λ, α, s + iτ) of the Lerch zeta-function for τ ∈ [T, T + H] where H ∈ [T27/82, T1/2]. The cases of all parameters, λ, α ∈ (0, 1], are considered. If the set {log(m + α) : m ∈ N0} is linearly independent over Q, then every analytic function in the strip {s= σ + it ∈ C : σ ∈ (1/2, 1)} is approximated by the above shifts. |
| Published | Basel : MDPI |
| Type | Journal article |
| Language | English |
| Publication date | 2025 |
| CC license |
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