Pairs of additive quadratic forms modulo one

 Access to full text

 Full (PDF)

1. [1] R. C. Baker, Small solutions of congruences, Mathematika 20 (1983), 164-188. Zbl0532.10011
2. [2] R. C. Baker, Diophantine Inequalities, Oxford University Press, Oxford 1986. Zbl0592.10029
3. [3] R. C. Baker and J. Brüdern, Pairs of quadratic forms modulo one, Glasgow Math. J., to appear. Zbl0774.11031
4. [4] R. C. Baker and J. Gajraj, On the fractional parts of certain additive forms, Math. Proc. Cambridge Philos. Soc. 79 (1976), 463-467. Zbl0323.10032
5. [5] R. C. Baker and G. Harman, Small fractional parts of quadratic and additive forms, Math. Proc. Cambridge Philos. Soc. 90 (1981), 5-12. Zbl0466.10029
6. [6] R. C. Baker and G. Harman, Small fractional parts of quadratic forms, Proc. Edinburgh Math. Soc. 25 (1982), 269-277. Zbl0499.10037
7. [7] R. J. Cook, The fractional parts of an additive form, Proc. Cambridge Philos. Soc. 72 (1972), 209-212. Zbl0237.10023
8. [8] I. Danicic, Contributions to number theory, Ph. D. thesis, London 1957. 
9. [9] I. Danicic, An extension of a theorem of Heilbronn, Mathematika 5 (1958), 30-37. Zbl0085.03304
10. [10] I. Danicic, On the fractional parts of θx² and ϕx², J. London Math. Soc. 34 (1959), 353-357. Zbl0088.25704
11. [11] I. Danicic, The distribution (mod 1) of pairs of quadratic forms with integer variables, J. London Math. Soc. 42 (1967), 618-623. Zbl0165.36402
12. [12] G. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge University Press, Cambridge 1967. 
13. [13] G. Harman, Diophantine approximation and prime numbers, Ph.D. thesis, London 1982. Zbl0443.10015
14. [14] D. R. Heath-Brown, Small solutions of quadratic congruences II, Mathematika 38 (1991), 264-284. Zbl0725.11018
15. [15] H. Heilbronn, On the distribution of the sequence θn² (mod 1), Quart. J. Math. Oxford Ser. (2) 19 (1948), 249-256. Zbl0031.20502
16. [16] M. C. Liu, On the fractional parts of $\theta n^k$ and $\varphi n^k$, Quart. J. Math. Oxford Ser. (2) 21 (1970), 481-486. 
17. [17] M. C. Liu, Simultaneous approximation of two additive forms, Trans. Amer. Math. Soc. 206 (1975), 361-373. Zbl0305.10024
18. [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. Zbl0446.10026
19. [19] W. M. Schmidt, Small fractional parts of polynomials, CBMS Regional Conf. Ser. in Math. 32, Amer.Math. Soc., Providence 1977.