Quadratic forms with cube-free discriminant
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- by Donald G. James
- Proc. Amer. Math. Soc. 110 (1990), 45-52
- DOI: https://doi.org/10.1090/S0002-9939-1990-1027095-2
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Abstract:
Formulas are given for the number of genera of ${\mathbf {Z}}$-lattices with rank $n \geq 3$, signature $s$, and cube-free discriminant $\Delta$. The results are applied to study classification and orthogonal splittings in the indefinite case.References
- J. W. S. Cassels, Rational quadratic forms, London Mathematical Society Monographs, vol. 13, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1978. MR 522835
- Kwong-shin Chang, Diskriminanten und Signaturen gerader quadratischer Formen, Arch. Math. (Basel) 21 (1970), 59–65 (German). MR 268122, DOI 10.1007/BF01220879
- Larry J. Gerstein, Orthogonal splitting and class numbers of quadratic forms, J. Number Theory 5 (1973), 332–338. MR 325535, DOI 10.1016/0022-314X(73)90034-6
- Donald G. James, Diagonalizable indefinite integral quadratic forms, Acta Arith. 50 (1988), no. 3, 309–314. MR 960557, DOI 10.4064/aa-50-3-309-314
- Donald G. James, Orthogonal decompositions of indefinite quadratic forms, Rocky Mountain J. Math. 19 (1989), no. 3, 735–740. Quadratic forms and real algebraic geometry (Corvallis, OR, 1986). MR 1043245, DOI 10.1216/RMJ-1989-19-3-735
- Donald G. James, Even quadratic forms with cube-free discriminant, Proc. Amer. Math. Soc. 106 (1989), no. 1, 73–79. MR 955998, DOI 10.1090/S0002-9939-1989-0955998-5 O. T. O’Meara, Introduction to quadratic forms, Springer-Verlag, New York, 1963.
- G. L. Watson, Integral quadratic forms, Cambridge Tracts in Mathematics and Mathematical Physics, No. 51, Cambridge University Press, New York, 1960. MR 0118704
Bibliographic Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 110 (1990), 45-52
- MSC: Primary 11E12
- DOI: https://doi.org/10.1090/S0002-9939-1990-1027095-2
- MathSciNet review: 1027095