Effective version of Tartakowsky's Theorem

• Autorzy: J. S. Hsia , M. I. Icaza
• Języki publikacji: EN

Kategorie tematyczne

• 11E39: Bilinear and Hermitian forms
• 11E12: Quadratic forms over global rings and fields
• 11D85: Representation problems
• 11E25: Sums of squares and representations by other particular quadratic forms

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 89
• Numer: 3
• Strony: 235-253

Daty

wydano

1999

otrzymano

1998-08-11

Twórcy

autor

J. S. Hsia

• Department of Mathematics, Ohio State University, 231 W. 18th Avenue, Columbus, Ohio 43210-1174, U.S.A.

autor

M. I. Icaza

• Instituto de Matematica y Fisica, Universidad de Talca, Avenida Lircay s/n, Talca, Chile

Bibliografia

• [BI] R. Baeza and M. I. Icaza, Decomposition of positive definite integral quadratic forms as sums of positive definite quadratic forms, in: Proc. Sympos. Pure Math. 58, Amer. Math. Soc., 1995, 63-72.
• [BH] J. W. Benham and J. S. Hsia, Spinor equivalence of quadratic forms, J. Number Theory 17 (1983), 337-342.
• [C] J. W. S. Cassels, Rational Quadratic Forms, Academic Press, 1978.
• [HKK] J. S. Hsia, Y. Kitaoka and M. Kneser, Representations by positive definite quadratic forms, J. Reine Angew. Math. 301 (1978), 132-141.
• [Hu] P. Humbert, Réduction de formes quadratiques dans un corps algébrique fini, Comment. Math. Helv. 23 (1949), 50-63.
• [Ki1] Y. Kitaoka, Siegel Modular Forms and Representation by Quadratic Forms, Tata Lecture Notes, Springer, 1986.
• [Ki2] Y. Kitaoka, A note on representation of positive definite binary quadratic forms by positive definite quadratic forms in 6 variables, Acta Arith. 54 (1990), 317-322.
• [Ki3] Y. Kitaoka, Arithmetic of Quadratic Forms, Cambridge Univ. Press, 1993.
• [Kn] M. Kneser, Quadratische Formen, Göttingen Lecture Notes, 1973/74.
• [N] G. L. Nipp, Quaternary Quadratic Forms - Computer Generated Tables, Springer, 1991.
• [OM1] O. T. O'Meara, The integral representations of quadratic forms over local rings, Amer. J. Math. 86 (1958), 843-878.
• [OM2] O. T. O'Meara, Introduction to Quadratic Forms, Springer, 1973.
• [T] W. Tartakowsky, Die Gesamtheit der Zahlen, die durch eine positive quadratische Form $F(x₁, ..., x_s)$ (s ≥ 4) darstellbar sind, Izv. Akad. Nauk SSSR 7 (1929), 111-122, 165-195.
• [W] G. L. Watson, Quadratic diophantine equations, Philos. Trans. Roy. Soc. London Ser. A 253 (1960), 227-254.