Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

Small fractional parts of quadratic forms

R. C. Bakera1 and G. Harmana1*

a1 Royal Holloway College, Egham, Surrey

Let xs2016xxs2016 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

S0013091500016758_eqnU1

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 form Q(x1,…, xs) there exist integers n1,…,ns not all zero with |n1|,…,|nsN and with

S0013091500016758_eqn1

(Received February 11 1981)

Footnotes

* Written while the second author held a University of London postgraduate studentship.