Hecke L-functions of certain subextensions in an extraspecial extension

Abstract

In 1925, Hecke found two different quadratic fields having the same $L$-functions attached to certain ray class groups. In this paper, we show that if $K/\mathbb{Q}$ is a Galois extension whose Galois group is isoclinic to an extraspecial group, then there are many elementary abelian extensions inside $K$ whose $L$-functions coincide.