Discrete Universality of the Derivatives of L-Functions of Elliptic Curves - Baravykienė, Daina; Garbaliauskas, Antanas; Garbaliauskienė, Virginija (Jaunųjų mokslininkų darbai, 2020)
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 arithmetical progression. We suppose that the number h > 0 is choosen so that exp{2πk/h} is an irrational number for all k ∈ Z \{0}. The proof of discrete universality of the derivative 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.
Keywords: elliptic curve; L-function of an elliptic curves; limit theorem; discrete universality