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International Algorithmic Number Theory Symposium

ANTS 2002: Algorithmic Number Theory pp 67–79Cite as

On Arithmetically Equivalent Number Fields of Small Degree

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2369))

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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Author information

Authors and Affiliations

  1. Mathematisch Instituut, Universiteit Nijmegen, Postbus 9010, 6500 GL, Nijmegen, the Netherlands

    Wieb Bosma

  2. Mathematisch Instituut, Universiteit Leiden, P. O. Box 9512, 2300 RA, Leiden, the Netherlands

    Bart de Smit

Authors
  1. Wieb Bosma
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  2. Bart de Smit
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Editor information

Editors and Affiliations

  1. School of Mathematics and Statistics, F07, University of Sydney, Sydney, NSW, 2006, Australia

    Claus Fieker  & David R. Kohel  & 

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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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  • DOI: https://doi.org/10.1007/3-540-45455-1_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43863-2

  • Online ISBN: 978-3-540-45455-7

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