Coincidence of $L$-functions
Volume 204 / 2022
Acta Arithmetica 204 (2022), 369-385
MSC: Primary 11R42; Secondary 11R32, 11R21, 12F12.
DOI: 10.4064/aa211012-14-6
Published online: 8 August 2022
Abstract
By the coincidence of $L$-functions, we mean an incident that the Hecke $L$-functions of ray class groups of several different fields coincide up to a finite number of Euler factors. This phenomenon was first observed by Hecke in 1925 for the case of quadratic fields. In this paper, we give a condition for the coincidence in the case of cyclic fields of prime degree in terms of Galois groups of certain abelian extension of the cyclic fields.
