A Discrete Limit Theorem for L-Functions of Elliptic Curves
Physical Sciences
Virginija Garbaliauskienė
Siauliai University
Antanas Garbaliauskas
Šiauliai State College
Published 2018-12-20
https://doi.org/10.21277/jmd.v48i2.224
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Keywords

elliptic curve
L-function
limit theorem
weak convergence

How to Cite

Garbaliauskienė V. and Garbaliauskas A. (2018) “A Discrete Limit Theorem for L-Functions of Elliptic Curves”, Jaunųjų mokslininkų darbai, 48(2), pp. 27-29. doi: 10.21277/jmd.v48i2.224.

Abstract

In the paper, we prove the discrete limit theorem in the sense of the weak convergence of probability measures in the space of analytic on DV = {s ∈ C : 1 < σ < 3/2, |t| <  V} functions for L-functions of elliptic curves LE(s). The main statement of the paper is as follows. Let h > 0 be a fixed real number such that exp {2πk/h} is an irrational number for all k∈Z\{0}. Then the probability measure μN(LE(s + imh)∈A), A ∈ B(H(DV)), converges weakly to the measure PLE as N→∞.

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