Lecture Notes in Computer Science, 2002, Volume 2369/2002, 43-55, DOI: 10.1007/3-540-45455-1_6

On Arithmetically Equivalent Number Fields of Small Degree

Wieb Bosma and Bart de Smit

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Abstract

For each integer n, let $ \mathcal{S}_n $ \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 $ \mathcal{S}_n , for small n. For example, for every x $ \mathcal{S}_n $ \mathcal{S}_n with n ≤ 15, x or x -1 is an integer that is a prime power dividing 214.36.53.

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