DISCRETE UNIVERSALITY OF THE DERIVATIVES OF L-FUNCTIONS OF ELLIPTIC CURVES Cover Image

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

Author(s): Daina Baravykienė, Antanas Garbaliauskas, Virginija Garbaliauskienė
Subject(s): Business Economy / Management, Higher Education
Published by: Vilniaus Universiteto Leidykla
Keywords: elliptic curve; L-function of elliptic curves; limit theorem; discrete universality;

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.

  • Issue Year: 2020
  • Issue No: 2 (50)
  • Page Range: 46-50
  • Page Count: 5
  • Language: Lithuanian