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THE DENSITY OF NUMBERS REPRESENTED BY DIAGONAL FORMS OF LARGE DEGREE
Published online by Cambridge University Press: 23 April 2018
Abstract
Let $s\geqslant 3$ be a fixed positive integer and let
$a_{1},\ldots ,a_{s}\in \mathbb{Z}$ be arbitrary. We show that, on average over
$k$, the density of numbers represented by the degree
$k$ diagonal form
$$\begin{eqnarray}a_{1}x_{1}^{k}+\cdots +a_{s}x_{s}^{k}\end{eqnarray}$$
$k$.
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- Copyright © University College London 2018