A Discrete Limit Theorem for L-Functions of Elliptic Curves

Jaunųjų Mokslininkų Darbai

Virginija Garbaliauskienė¹  Antanas Garbaliauskas² 

[1] Siauliai University;Šiauliai State College;

关键词: elliptic curve;    L-function;    limit theorem;    weak convergence;   

DOI  :  10.21277/jmd.v48i2.224

来源: DOAJ

【 摘 要 】

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→∞.

【 授权许可】

Unknown