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Zur Darstellung definiter Funktionen als Summe von Quadraten. (To the representation of definite functions as the sum of squares). (German) Zbl 0222.10022


MSC:

11E25 Sums of squares and representations by other particular quadratic forms
11R58 Arithmetic theory of algebraic function fields
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References:

[1] Artin, E.: Über die Zerlegung definiter Funktionen in Quadrate. Hamb. Abh.5, 100-115 (1927) =Collected Papers 273-288. · doi:10.1007/BF02952513
[2] Ax, J.: On ternary definite rational functions. (To appear in Proc. London Math. Soc.) · Zbl 0266.14018
[3] Cassels, J. W. S.: On the representation of rational functions as sums of squares. Acta Arithm.9, 79-82 (1964). · Zbl 0131.25001
[4] Hilbert, D.: Über die Darstellung definiter Formen als Summe von Formenquadraten. Math. Ann.32, 342-350 (1888) =Ges. Abh. II, 154-161. · doi:10.1007/BF01443605
[5] ?: Über ternäre definite Formen. Acta Math.17, 169-197 (1993) =Ges. Abh. II, 345-366. · doi:10.1007/BF02391990
[6] Hilbert, D. Mathematische Probleme. Göttinger Nachr. 1900, 253-297 =Ges. Abh. III, 290-329.
[7] Landau, E.: Über die Darstellung definiter Funktionen durch Quadrate. Math. Ann.62, 272-285 (1906). · doi:10.1007/BF01449981
[8] Lang, S.: On quasi-algebraic closure. Ann. of Math.55, 373-390 (1952). · Zbl 0046.26202 · doi:10.2307/1969785
[9] ? The theory of real places. Ann. of Math.57, 378-391 (1953). · Zbl 0052.03301 · doi:10.2307/1969865
[10] Pfister, A.: Darstellung von ? 1 als Summe von Quadraten in einem Körper. London J. of Math.40, 159-165 (1965). · Zbl 0131.25002 · doi:10.1112/jlms/s1-40.1.159
[11] Pfister, A.: Multiplikative quadratische Formen. Arch. Math.16, 363-370 (1965). · Zbl 0146.26001 · doi:10.1007/BF01220043
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