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

In this paper, we show that an action on the set of elliptic curves with j = 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. [ABSTRACT FROM AUTHOR]