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Transactions of the American Mathematical Society

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Theory of reduction for arithmetical equivalence


Author: Hermann Weyl
Journal: Trans. Amer. Math. Soc. 48 (1940), 126-164
MSC: Primary 10.0X
DOI: https://doi.org/10.1090/S0002-9947-1940-0002345-2
MathSciNet review: 0002345
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References [Enhancements On Off] (What's this?)

  • [1] Journal für die reine und angewandte Mathematik, vol. 129 (1905), pp. 220-274; also Gesammelte Abhandlungen II, Leipzig, 1911, pp. 53-100. Cited as M with the page number in the Gesammelte Abhandlungen.
  • [2] Sitzungsberichte der Preussischen Akademie der Wissenschaften, 1928, pp. 510-535; 1929, p. 508.
  • [3] Quarterly Journal of Mathematics, vol. 9 (1938), pp. 259-262.
  • [4] Hermann Weyl, On geometry of numbers, Proc. London Math. Soc. (2) 47 (1942), 268–289. MR 0006212, https://doi.org/10.1112/plms/s2-47.1.268
  • [5] Another short proof by H. Davenport, Quarterly Journal of Mathematics, vol. 10 (1939), pp. 119-121.
  • [6] Compositio Mathematica, vol. 5 (1938), pp. 368-391.
  • [7] Cf. Minkowski's definition in $ {\text{M}}$, p. 59.
  • [8] See Mahler, loc. cit. (3 above), and the author, loc. cit. (4 above), Theorem V.
  • [9] Weyl, loc. cit. (4 above), ``Generalized Theorem V."
  • [10] See M, pp. 56-58.
  • [11] For more details see L. E. Dickson, Algebren und ihre Zahlentheorie, Zürich, 1927, chap. 9; C. G. Latimer, American Journal of Mathematics, vol. 48 (1926), pp. 57-66; M. Deuring, Algebren, Ergebnisse der Mathematik, vol. 4, no. 1, Berlin, 1935, chap. 6.
  • [12] Vorlesungen über die Zahlentheorie der Quaternionen, Berlin, 1919.
  • [13] The larger part of E. H. Moore's ``Algebra of Matrices'' (General Analysis, Part I, Memoirs of the American Philosophical Society, Philadelphia, 1935) deals with the formalism of ``Hamiltonian'' forms.
  • [14] Cf. Weyl, loc. cit. (4 above), §8, and the more complicated argument in Bieberbach-Schur, loc. cit. (2 above), pp. 521-523.
  • [15] Loc. cit. (6 above), equation (25).
  • [16] See M, p. 53.

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DOI: https://doi.org/10.1090/S0002-9947-1940-0002345-2
Article copyright: © Copyright 1940 American Mathematical Society