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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Theory of reduction for arithmetical equivalence

Author: Hermann Weyl
Journal: Trans. Amer. Math. Soc. 48 (1940), 126-164
MSC: Primary 10.0X
MathSciNet review: 0002345
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    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. Sitzungsberichte der Preussischen Akademie der Wissenschaften, 1928, pp. 510-535; 1929, p. 508. Quarterly Journal of Mathematics, vol. 9 (1938), pp. 259-262.
  • Hermann Weyl, On geometry of numbers, Proc. London Math. Soc. (2) 47 (1942), 268–289. MR 6212, DOI
  • Another short proof by H. Davenport, Quarterly Journal of Mathematics, vol. 10 (1939), pp. 119-121. Compositio Mathematica, vol. 5 (1938), pp. 368-391. Cf. Minkowski’s definition in ${\text {M}}$, p. 59. See Mahler, loc. cit. (3 above), and the author, loc. cit. (4 above), Theorem V. Weyl, loc. cit. (4 above), “Generalized Theorem V." See M, pp. 56-58. 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. Vorlesungen über die Zahlentheorie der Quaternionen, Berlin, 1919. 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. Cf. Weyl, loc. cit. (4 above), §8, and the more complicated argument in Bieberbach-Schur, loc. cit. (2 above), pp. 521-523. Loc. cit. (6 above), equation (25). See M, p. 53.

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