Date: 21 Jun 2002

On Arithmetically Equivalent Number Fields of Small Degree

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Abstract

For each integer n, let \( \mathcal{S}_n \) be the set of all class number quotients h(K)/h(K) for number fields K and K of degree n with the same zeta-function. In this note we will give some explicit results on the finite sets \( \mathcal{S}_n \) , for small n. For example, for every x\( \mathcal{S}_n \) with n ≤ 15, x or x -1 is an integer that is a prime power dividing 214.36.53.