Nagoya Mathematical Journal

On maximal orders of division quaternion algebras over the rational number field with certain optimal embeddings

Tomoyoshi Ibukiyama

Full-text: Open access

Article information

Source
Nagoya Math. J. Volume 88 (1982), 181-195.

Dates
First available in Project Euclid: 14 June 2005

Permanent link to this document
http://projecteuclid.org/euclid.nmj/1118787011

Mathematical Reviews number (MathSciNet)
MR0683249

Zentralblatt MATH identifier
0473.12012

Subjects
Primary: 11R52: Quaternion and other division algebras: arithmetic, zeta functions
Secondary: 16A45

Citation

Ibukiyama, Tomoyoshi. On maximal orders of division quaternion algebras over the rational number field with certain optimal embeddings. Nagoya Math. J. 88 (1982), 181--195. http://projecteuclid.org/euclid.nmj/1118787011.


Export citation

References

  • [1] A. A. Albert, Integral domains of rational generalized quaternion algebras, Bull. Amer. Math. Soc, 40 (1934), 164-176.
  • [2] M. Deuring, Die Typen der Multiplikatorenringe elliptischen Funktionen-korper, Abh. Hamburg, 14 (1941), 197-272.
  • [3] M. Deuring, Die Anzahl der Typen von Maximalordnungen einer deiniten Quaternionen- algebra mit primer Grundzahl, Jahresbericht der Deutschen Math., 54 (1951), 24-41.
  • [4] M. Eiehler, ber die Idealklassenzahl total definiter Quaternionenalgebren, Math. Z., 43 (1938), 102-109.
  • [5] M. Eiehler, Zur Zahlentheorie der Quaternionen-Algebren, J. reine angew. Math., 195 (1955), 127-151.
  • [6] K. Hashimoto, Twisted trace formula of the Brandt matrix, Proc. Japan Acad., 53, Ser. A (1977), 98-102.
  • [7] K. Hashimoto, Some examples of integral definite quaternary quadratic forms with prime discriminant, Nagoya Math. J., 77 (1980), 167-175.
  • [8] T. Ibukiyama, A basis and maximal orders in quaternion algebras over the rational number field (in Japanese), Sugaku, 24 (1972), 316-318.
  • [9] P. Ponomarev, A correspondence between quaternary quadratic forms, Nagoya Math. J., 62 (1976), 125-140.
  • [10] H. Shimizu, On zeta functions of quaternion algebras, Ann. Math., 81 (1965), 166-193.
  • [11] H. Shimizu, Some examples of new forms, J. Fac. Sci. Univ. Tokyo, 24-1 (1977), 97-113. Department of Mathematics Faculty of Science University of Tokyo Hongo, Tokyo 113 Japan Department of Mathematics College of General Education Kyushu University Chuo-ku, Fukuoka 810 Japan