On the Generalizations of Universality Theorem for L-Functions of Elliptic Curves

Abstract

In the paper, the continuous type’s universality theorem for L-functions of elliptic curves is discussed and its generalizations in three directions – for positive integer powers and derivatives of L-functions of elliptic curves as well as the weighted universality theorem of L-functions of elliptic curves – are given. The proofs of the universality are based on limit theorems in the sense of weak convergence of probability measures in functional spaces.

Keywords

• elliptic curve
• L-function
• universality