Distribution of root numbers of Hecke characters attached to some elliptic curves

Abstract

In this paper, we show that an action on the set of elliptic curves with j=1728j=1728 preserves a certain kind of symmetry on the local root number of Hecke characters attached to such elliptic curves. As a consequence, we give results on the distribution of the root numbers and their average of the aforementioned Hecke characters. © 2021 Walter de Gruyter GmbH, Berlin/Boston 2021.