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Baravykienė, Daina; Garbaliauskas, Antanas; Garbaliauskienė, Virginija
Jaunųjų Mokslininkų Darbai, 12/2020, Volume: 50, Issue: 2 (50)Journal Article
In the paper, we prove the discrete universality theorem in the sense of the weak convergence of probability measures in the space of analytic functions for the derivatives of L-functions of elliptic curves. We consider an approximation of analytic functions by translations L‘E (s + imh), where h > 0 is a fixed number, the translations of the imaginary part of the complex variable take values from some discrete set such as arithmetical progression. We suppose that the number h > 0 is chosen so that exp{2πk/h } is an irrational number for all k ∈ Z \{0} . The proof of discrete universality of the derivatives of L-functions of elliptic curves is based on a limit theorem in the sense of weak convergence of probability measures in the space of analytic functions.
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