Pairs of additive quadratic forms modulo one

• Autorzy: R. C. Baker , S. Schäffer
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1992
• Tom: 62
• Numer: 1
• Strony: 45-59

Daty

wydano

1992

otrzymano

1991-06-24

poprawiono

1991-07-26

Twórcy

autor

R. C. Baker

• Department of Mathematics, Royal Holloway and Bedford New College, Egham, Surrey TW20 OEX, U.K.

autor

S. Schäffer

• Am Pastorenholz 8, 4972 Löhne, Germany

Bibliografia

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• [2] R. C. Baker, Diophantine Inequalities, Oxford University Press, Oxford 1986.
• [3] R. C. Baker and J. Brüdern, Pairs of quadratic forms modulo one, Glasgow Math. J., to appear.
• [4] R. C. Baker and J. Gajraj, On the fractional parts of certain additive forms, Math. Proc. Cambridge Philos. Soc. 79 (1976), 463-467.
• [5] R. C. Baker and G. Harman, Small fractional parts of quadratic and additive forms, Math. Proc. Cambridge Philos. Soc. 90 (1981), 5-12.
• [6] R. C. Baker and G. Harman, Small fractional parts of quadratic forms, Proc. Edinburgh Math. Soc. 25 (1982), 269-277.
• [7] R. J. Cook, The fractional parts of an additive form, Proc. Cambridge Philos. Soc. 72 (1972), 209-212.
• [8] I. Danicic, Contributions to number theory, Ph. D. thesis, London 1957.
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• [10] I. Danicic, On the fractional parts of θx² and ϕx², J. London Math. Soc. 34 (1959), 353-357.
• [11] I. Danicic, The distribution (mod 1) of pairs of quadratic forms with integer variables, J. London Math. Soc. 42 (1967), 618-623.
• [12] G. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge University Press, Cambridge 1967.
• [13] G. Harman, Diophantine approximation and prime numbers, Ph.D. thesis, London 1982.
• [14] D. R. Heath-Brown, Small solutions of quadratic congruences II, Mathematika 38 (1991), 264-284.
• [15] H. Heilbronn, On the distribution of the sequence θn² (mod 1), Quart. J. Math. Oxford Ser. (2) 19 (1948), 249-256.
• [16] M. C. Liu, On the fractional parts of $θn^k$ and $ϕn^k$, Quart. J. Math. Oxford Ser. (2) 21 (1970), 481-486.
• [17] M. C. Liu, Simultaneous approximation of two additive forms, Trans. Amer. Math. Soc. 206 (1975), 361-373.
• [18] A. Schinzel, H. P. Schlickewei and W. M. Schmidt, Small solutions of quadratic congruences and small fractional parts of quadratic forms, Acta Arith. 37 (1980), 241-248.
• [19] W. M. Schmidt, Small fractional parts of polynomials, CBMS Regional Conf. Ser. in Math. 32, Amer.Math. Soc., Providence 1977.