Arithmetic of Orthogonal Groups

Takashi ONO

doi:10.2969/jmsj/00710079

Takashi ONO

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1955 Volume 7 Issue 1 Pages 79-91

DOI https://doi.org/10.2969/jmsj/00710079

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Published: 1955 Received: June 28, 1954 Available on J-STAGE: August 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: August 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) H. Hasse, Über die Darstellbarkeit von Zahlen durch quadratische Formen im Körper der rationalen Zahlen, Crelle, Bd. 152, pp. 129-148, 1923.
2) H. Hasse, Über die Äquivalenz quadratischer Formen im Korper der rationalen Zahlen, Crelle, Crelle, Bd. pp. 205-224.
3) M. Deuring, Algebren, Ergebn, d. Math. IV, 1. Berlin, 1935.
4) E. Witt, Theorie der quadratischen Formen in beliebigen Körpern, Crelle, Bd. 176, pp. 31-44, 1937.
5) J. Dieudonné, Sur les grouper classiques, Actual. Scient. et Ind., no. 1040, Paris (Hermann), 1948.
6) M. Eichler, Quadratische Formen and Orthogonale Gruppen, Berlin (Springer), 1952.
7) L. E. Dickson, Linear groups, Leipzig (Teubner), 1901.
8) B. W. Jones, The Arithmetic Theory of Quadratic Forms, New York, 1950.
9) E: Artin, Algebraic numbers and algebraic functions I, Princeton, 1951.
10) T. Ono, On the Compacity of the Orthogonal groups, Nagoya Math. Journ., vol. 7, 1954.
11) J. Dieudonné, On the automorphisms of the classical groups, Memoirs of the Amer. Math. Soc. vol. 2., 1952.
12) C. Chevalley, Sur la théorie du corps de classes dans les corps finis et les corps locaux, Journ. Fac. Sci. Tokyo II, pp. 365-474, 1933.
13) C. E. Rickart, Isomorphic groups of linear transformations II, Amer. Journ, of Math. vol. 73., pp. 697-716, 1951.

Right : [1] H. Hasse, Über die Darstellbarkeit von Zahlen durch quadratische Formen im Körper der rationalen Zahlen, Crelle, Bd. 152, pp. 129-148, 1923.
[2] H. Hasse, Über die Äquivalenz quadratischer Formen im Korper der rationalen Zahlen, Crelle, Crelle, Bd. pp. 205-224.
[3] M. Deuring, Algebren, Ergebn, d. Math. IV, 1. Berlin, 1935.
[4] E. Witt, Theorie der quadratischen Formen in beliebigen Körpern, Crelle, Bd. 176, pp. 31-44, 1937.
[5] J. Dieudonné, Sur les groupes classiques, Actual. Scient. et Ind., no. 1040, Paris (Hermann), 1948.
[6] M. Eichler, Quadratische Formen und Orthogonale Gruppen, Berlin (Springer), 1952.
[7] L. E. Dickson, Linear groups, Leipzig (Teubner), 1901.
[8] B. W. Jones, The Arithmetic Theory of Quadratic Forms, New York, 1950.
[9] E: Artin, Algebraic numbers and algebraic functions I, Princeton, 1951.
[10] T. Ono, On the Compacity of the Orthogonal groups, Nagoya Math. Journ., vol. 7, 1954.
[11] J. Dieudonné, On the automorphisms of the classical groups, Memoirs of the Amer. Math. Soc. vol. 2., 1952.
[12] C. Chevalley, Sur la théorie du corps de classes dans les corps finis et les corps locaux, Journ. Fac. Sci. Tokyo II, pp. 365-474, 1933.
[13] C. E. Rickart, Isomorphic groups of linear transformations II, Amer. Journ, of Math. vol. 73., pp. 697-716, 1951.

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