A Discrete Limit Theorem for L-Functions of Elliptic Curves - Garbaliauskienė, Virginija; Garbaliauskas, Antanas (Jaunųjų mokslininkų darbai, 2018)
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→∞.