Geodesic
Pairs of quadratic forms modulo one
Glasgow mathematical journal, Tome 35 (1993) no. 1, pp. 51-61

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Let s be a natural number, s ≥ 2. We seek a positive number λ(s) with the following property:Let ε > 0. Let Q1(x1, ..., xs), Q2(x1, ..., xs) be real quadratic forms, then for N > C1(s, ε) we havefor some integers n1, ..., ns, 
Baker, R. C.; Brüdern, J. Pairs of quadratic forms modulo one. Glasgow mathematical journal, Tome 35 (1993) no. 1, pp. 51-61. doi: 10.1017/S0017089500009551
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[1] 1.Baker, R. C., Diophantine inequalities, (Oxford University Press, 1986). Google Scholar

[2] 2.Baker, R. C. and Harman, G., Small fractional parts of quadratic and additive forms, Math. Proc. Camb. Phil Soc. 90 (1981), 5–12. Google Scholar | DOI

[3] 3.Baker, R. C. and Harman, G., Small fractional parts of quadratic forms, Proc. Edinburgh Math. Soc., 25 (1982), 269–277. Google Scholar

[4] 4.Baker, R. C. and Schäffer, S.. Pairs of additive quadratic forms modulo one. Submitted to Acta Arith. Google Scholar

[5] 5.Danicic, I., An extension of a theorem of Heilbronn. Mathematika, 5 (1958), 30–37. Google Scholar

[6] 6.Danicic, I., The distribution (mod 1) of pairs of quadratic forms with integer variables, J. London Math. Soc. 42 (1967), 618–623. Google Scholar | DOI

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

[8] 8.Davenport, H., Indefinite quadratic forms in many variables II, Proc. London Math. Soc. (3), 8 (1958), 109–126. Google Scholar

[9] 9.Heath-Brown, D. R.. Small solutions of quadratic congruences, II. Mathematika, to appear. Google Scholar

[10] 10.Schinzel, A., Schlickewei, H. P. and Schmidt, W. M., Small solutions of quadratic congruences and small fractional parts of quadratic forms, Acta Arith. 37 (1980), 241–248. Google Scholar

[11] 11.Schmidt, W. M., Small fractional parts of polynomials, Regional Conference Series No. 32, American Math. Soc, Providence 1977. Google Scholar

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