Geodesic
Indefinite quadratic polynomials
Glasgow mathematical journal, Tome 24 (1983) no. 2, pp. 133-138

Voir la notice de l'article provenant de la source Cambridge University Press

Letbe an indefinite quadratic form with real coefficients. A well-known result, due to Birch, Davenport and Ridout [1], [5] and [6], states that if n ≥21 then for any ε > 0 there is an integer vector x ≠O such thatRecently [3] we have quantified this result, obtaining a function g(n) such that g(n)→ 1⁄2 as n n→ ∞ and such that for any η > 0 and all large enough X there is an integer vector x satisfyingwhere |x| = max |xi|and the implicit constant in Vinogradov's ≪-notation is independent of X. 
Cook, R. J. Indefinite quadratic polynomials. Glasgow mathematical journal, Tome 24 (1983) no. 2, pp. 133-138. doi: 10.1017/S0017089500005206
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[1] 1.Birch, B. J. and Davenport, H., Indefinite quadratic forms in many variables, Mathematika 5 (1958), 8–12. Google Scholar | DOI

[2] 2.Birch, B. J. and Davenport, H., On a theorem of Davenport and Heilbronn, Acta Math. 100 (1958), 259–279. Google Scholar | DOI

[3] 3.Cook, R. J., Small values of indefinite quadratic forms and polynomials in many variables (submitted for publication). Google Scholar

[4] 4.Davenport, H., Indefinite quadratic forms in many variables, Mathematika 3 (1956), 81–101. Google Scholar | DOI

[5] 5.Davenport, H. and Ridout, D., Indefinite quadratic forms, Proc. London Math. Soc. (3) 9 (1959), 554–555. Google Scholar

[6] 6.Ridout, D., Indefinite quadratic forms, Mathematika 5 (1958), 122–124. Google Scholar | DOI

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