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Small fractional parts of quadratic forms

Published online by Cambridge University Press:  20 January 2009

R. C. Baker  and
G. Harman
R. C. Baker
Affiliation:
Royal Holloway College, Egham, Surrey
G. Harman
Affiliation:
Royal Holloway College, Egham, Surrey
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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|,…,|ns≦N and with

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 25 , Issue 3 , October 1982 , pp. 269 - 277
Copyright
Copyright © Edinburgh Mathematical Society 1982

References

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