On arithmetically equivalent number fields of small degree

Abstract

For each integer n, let Sn be the set of all class number quotients h(K)/h(Kʹ) for number fields K and Kʹ of degree n with the same zeta-function. In this note we will give some explicit results on the finite sets Sn, for small n. For example, for every x ∈ Sn with n ≤ 15, x or x−1 is an integer that is a prime power dividing 214 ・ 36 ・ 53.