On Arithmetically Equivalent Number Fields of Small Degree

  • Wieb Bosma
  • Bart de Smit
Conference paper

DOI: 10.1007/3-540-45455-1_6

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

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Wieb Bosma
    • 1
  • Bart de Smit
    • 2
  1. 1.Mathematisch InstituutUniversiteit NijmegenNijmegenthe Netherlands
  2. 2.Mathematisch InstituutUniversiteit LeidenLeidenthe Netherlands

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