Elipsinių kreivių L funkcijų diskrečiojo universalumo tyrimas
The Investigation of the Discrete Universality 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 L-functions of elliptic curves. We consider an approximation of analytic functions by translations Lg(s+imh), where h > 0 is a fixed number, m takes values from some discrete set such as arithmetical progression. We suppose that the number h > 0 is chosen so that exp{2πk/h } is a rational number for some k∈Z \ {0}. The proof of discrete universality 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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