Advertisement

On the density theorem related to the space of non-split tri-Hermitian forms II

  • Akihiko YukieEmail author
Article

Abstract

Let \({\widetilde{k}}\) be a fixed cubic field, F a quadratic field and \(L=\widetilde{k}\cdot F\). In this paper and its companion paper, we determine the density of more or less the ratio of the residues of the Dedekind zeta functions of LF where F runs through quadratic fields.

Mathematics Subject Classification

11S90 11R45 20G25 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

References

  1. 1.
    Greenberg, M.J.: Lectures on Forms on Many Variables. Mathematics Lecture Note Series. Benjamin, New York (1969)Google Scholar
  2. 2.
    Kable, A.C., Yukie, A.: Prehomogeneous vector spaces and field extensions II. Invent. Math. 130(2), 315–344 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Kable, A.C., Yukie, A.: The mean value of the product of class numbers of paired quadratic fields I. Tohoku Math. J. 54(4), 513–565 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Kable, A.C., Yukie, A.: The mean value of the product of class numbers of paired quadratic fields II. J. Math. Soc. Japan 55(3), 739–764 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Kable, A.C., Yukie, A.: The mean value of the product of class numbers of paired quadratic fields. III. J. Number Theory 99(1), 185–218 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Kato, R., Yukie, A.: Rational orbits of the space of pairs of exceptional Jordan algebras. J. Number Theory 189, 304–352 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Wright, D.J.: The adelic zeta function associated to the space of binary cubic forms part I: global theory. Math. Ann. 270, 503–534 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Yukie, A.: On the density theorem related to the space of non-split tri-Hermitian forms I. J. Number Theory 194, 117–169 (2019)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Graduate School of ScienceKyoto UniversityKyotoJapan

Personalised recommendations