A Weighted Universality Theorem for L-Functions of Elliptic Curves

Abstract

In the paper, a short survey on universality results for L-functions of elliptic curves over the field of rational numbers is given and weighted universality theorem is proven. All stated universality theorems are of continuous type. The proof of the universality for 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.

A Weighted Discrete Universality Theorem for Periodic Zeta-Functions. Ii

“…In [8], a weighted universality theorem for the Riemann zeta-function was obtained. Generalizations of a theorem of such a type were given in [9] and [4]. The weighted universality for the function ζ(s; a) was began to study in [18].…”