Arithmetic of Hermitian Forms

@inproceedings{Shimura2008ArithmeticOH,
  title={Arithmetic of Hermitian Forms},
  author={Goro Shimura},
  year={2008}
}
We investigate the following two problems on a hermitian form Φ over an algebraic number field: (1) classification of Φ over the ring of algebraic integers; (2) hermitian Diophantine equations. The same types of problems for quadratic forms were treated in the author’s previous articles. Here we discuss the hermitian case. Problem (2) concerns an equation ξΦ · ξ = Ψ , where Φ and Ψ represent hermitian forms. We connect the number of such ξ modulo a group of units with the class number and mass… CONTINUE READING

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-9 of 9 references

Arithmetic and analytic theories of quadratic forms and Clifford groups

  • G. Shimura
  • Mathematical Surveys and Monographs,
  • 2004

Euler Products and Eisenstein series

  • G. Shimura
  • CBMS Regional Conference Series in Mathematics,
  • 1997

Arithmetic of unitary groups

  • G. Shimura
  • Ann. of Math.,
  • 1964

Zur Zahlentheorie der Quaternionen-Algebren

  • M. Eichler
  • J. reine angew. Math
  • 1956

Landherr , Äquivalenz Hermitscher Formen über einem beliebigen algebraischen Zahlkörper , Abh

  • W. GoroShimura
  • Math . Sem . Hamb .
  • 1936

Äquivalenz Hermitscher Formen über einem beliebigen algebraischen Zahlkörper

  • W. Landherr
  • Abh. Math. Sem. Hamb.,
  • 1936

Similar Papers

Loading similar papers…