## Theory of reduction for arithmetical equivalence

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- by Hermann Weyl
- Trans. Amer. Math. Soc.
**48**(1940), 126-164 - DOI: https://doi.org/10.1090/S0002-9947-1940-0002345-2
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## References

- Journal für die reine und angewandte Mathematik, vol. 129 (1905), pp. 220-274; also
- Hermann Weyl,
*On geometry of numbers*, Proc. London Math. Soc. (2)**47**(1942), 268–289. MR**6212**, DOI 10.1112/plms/s2-47.1.268
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,

*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.

*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.

## Bibliographic Information

- © Copyright 1940 American Mathematical Society
- 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