ELIPSINIŲ KREIVIŲ L FUNKCIJŲ IŠVESTINĖS DISKRETUSIS UNIVERSALUMAS
DISCRETE UNIVERSALITY OF THE DERIVATIVES OF L-FUNCTIONS OF ELLIPTIC CURVES

Summary/Abstract: 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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