Geodesic
On the Quantitative Sharpening of a Theorem of Birch
Matematičeskie zametki, Tome 88 (2010) no. 6, pp. 897-901

Voir la notice de l'article provenant de la source Math-Net.Ru

The author's results concerning the null subspaces of arbitrary odd polynomials in several variables are generalized to the case of common null subspaces for several odd polynomials as well as to the complex case.
Keywords: homogeneous polynomials, Birch's theorem, polynomials of odd degree, ordered partition of a set. 
T. Yu. Kulikova. On the Quantitative Sharpening of a Theorem of Birch. Matematičeskie zametki, Tome 88 (2010) no. 6, pp. 897-901. http://geodesic.mathdoc.fr/item/MZM_2010_88_6_a8/
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[1] B. J. Birch, “Homogeneous forms of odd degree in a large number of variables”, Mathematica, 4 (1957), 102–105 | MR | Zbl

[2] R. Aron, R. Gonzalo, A. Zagorodnyuk, “Zeroes of real polynomials”, Linear and Multilinear Algebra, 48:2 (2000), 107–115 | DOI | MR | Zbl

[3] T. D. Wooley, “Linear spaces on cubic hypersurfaces, and pairs of homogeneous cubic equations”, Bull. London Math. Soc., 29:5 (1997), 556–562 | DOI | MR | Zbl

[4] T. D. Wooley, “An explicit version of Birch's theorem”, Acta Arith., 85:1 (1998), 79–96 | MR | Zbl

[5] R. M. Aron, P. Hájek, “Zero sets of polynomials in several variables”, Arch. Math. (Basel), 86:6 (2006), 561–568 | MR | Zbl

[6] T. Yu. Kulikova, “Zamechanie o nulevykh podprostranstvakh nechetnykh polinomov”, Matem. zametki, 86:4 (2009), 543–549 | MR | Zbl