Universality Theorems in Physics

Garbaliauskas, Antanas

doi:10.21277/jmd.v48i2.223

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2022

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“…Rymano ir L funkcijų universalumas plačiai taikomas kvantinėje mechanikoje, kondensuotų medžiagų fizikoje bei statistinėje fizikoje [6].…”

Section: Discussionunclassified

The Investigation of the Discrete Universality of L-Functions of Elliptic Curves

Zakaitė,

Garbaliauskas

2022

JMD

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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 LE (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 rational number for some non-zero integer. 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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“…Rymano ir L funkcijų universalumas plačiai taikomas kvantinėje mechanikoje, kondensuotų medžiagų fizikoje bei statistinėje fizikoje [6].…”

Section: Discussionunclassified