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Computation of relative class numbers of imaginary cyclic fields of 2-power degrees

  • Stéphane Louboutin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1423)

Abstract

In this abridged version of [Lou], we outline an efficient technique for computing relative class numbers of imaginary abelian fields. It enables us to compute relative class numbers of imaginary cyclic fields of degrees 32 and conductors greater than 1013, or of degrees 4 and conductors greater than 1015. Our major innovation is a technique for computing numerically root numbers appearing in some functional equations.

Mathematics Subject Classification

11R20 11R29 11Y40 11M20 11R42 

Keywords

Imaginary abelian number field relative class number 

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References

  1. [BE]
    B.C. Berndt and R.J. Evans. The determination of Gauss sums. Bull. Amer. Math. Soc. 5 (2) (1981), 107–129.MATHMathSciNetCrossRefGoogle Scholar
  2. [Lou]
    S. Louboutin. Computation of relative class numbers of imaginary abelian number fields. Experimental Math, to appear.Google Scholar
  3. [Wa]
    L.C. Washington. Introduction to Cyclotomic Fields. Grad.Texts Math. 83, Springer-Verlag (1982); Second Edition: 1997.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Stéphane Louboutin
    • 1
  1. 1.UFR Sciences Département de MathématiquesUniversité de CaenCaen cedexFrance

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