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  • Cited by 4
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Baker, R. C. and Brüdern, J. 1993. Pairs of quadratic forms modulo one. Glasgow Mathematical Journal, Vol. 35, Issue. 01, p. 51.

    Heath-Brown, D. R. 1991. Small solutions of quadratic congruences, II. Mathematika, Vol. 38, Issue. 02, p. 264.

    1987. Geometry of Numbers.

    Baker, R. C. 1983. Small solutions of congruences. Mathematika, Vol. 30, Issue. 02, p. 164.

  • Proceedings of the Edinburgh Mathematical Society, Volume 25, Issue 3
  • October 1982, pp. 269-277

Small fractional parts of quadratic forms

  • R. C. Baker (a1) and G. Harman (a1)
  • DOI:
  • Published online: 01 January 2009

Let ‖x‖ denote the distance of x from the nearest integer. In 1948 H. Heilbronn proved [5] that for ε>0 and N>c1(ε) the inequality

holds for any real α. This result has since been generalised in many different directions, and we consider here extensions of the type: For ε>0, N>c2{ε, s) and a quadratic formQ(x1,…, xs) there exist integersn1,…,nsnot all zero with |n1|,…,|nsN and with

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6.H. L. Montgomery , The analytic principle of the large sieve, Bull. Amer. Math. Soc. 84 (1978), 547567.

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
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