On the Hasse principle for quadratic forms
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- by J. S. Hsia PDF
- Proc. Amer. Math. Soc. 39 (1973), 468-470 Request permission
Abstract:
Examples are given for rational function fields that do not satisfy the strong Hasse principle for quadratic forms.References
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Z. I. Borevič and I. R. Šafarevič, Number theory, “Nauka", Moscow, 1964; English transl., Pure and Appl. Math., vol. 20, Academic Press, New York, 1966. MR 30 #1080; MR 33 #4001.
- J. W. S. Cassels, W. J. Ellison, and A. Pfister, On sums of squares and on elliptic curves over function fields, J. Number Theory 3 (1971), 125–149. MR 292781, DOI 10.1016/0022-314X(71)90030-8
- J. S. Hsia and Robert P. Johnson, On the representation in sums of squares for definite functions in one variable over an algebraic number field, Amer. J. Math. 96 (1974), 448–453. MR 360467, DOI 10.2307/2373553
- Manfred Knebusch, Grothendieck- und Wittringe von nichtausgearteten symmetrischen Bilinearformen, S.-B. Heidelberger Akad. Wiss. Math.-Natur. Kl. 1969/70 (1969/1970), 93–157 (German). MR 0271118
- James T. Knight, Quadratic forms over $R(t)$, Proc. Cambridge Philos. Soc. 62 (1966), 197–205. MR 188161, DOI 10.1017/s030500410003975x
- John Milnor, Algebraic $K$-theory and quadratic forms, Invent. Math. 9 (1969/70), 318–344. MR 260844, DOI 10.1007/BF01425486 O. T. O’Meara, Introduction to quadratic forms, Die Grundlehren der math. Wissenschaften, Band 117, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 27 #2485.
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 39 (1973), 468-470
- MSC: Primary 10C05
- DOI: https://doi.org/10.1090/S0002-9939-1973-0311572-3
- MathSciNet review: 0311572