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.
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Bosma, W., de Smit, B. (2002). On Arithmetically Equivalent Number Fields of Small Degree. In: Fieker, C., Kohel, D.R. (eds) Algorithmic Number Theory. ANTS 2002. Lecture Notes in Computer Science, vol 2369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45455-1_6
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