5 research outputs found
Sums of arithmetic functions over values of binary forms
Given a suitable arithmetic function h, we investigate the average order of h
as it ranges over the values taken by an integral binary form F. A general
upper bound is obtained for this quantity, in which the dependence upon the
coefficients of F is made completely explicit.Comment: 12 page
Binary linear forms as sums of two squares
We revisit recent work of Heath-Brown on the average order of the quantity
r(L_1)r(L_2)r(L_3)r(L_4), for suitable binary linear forms L_1,..., L_4, for
integers ranging over quite general regions. In addition to improving the error
term in Heath-Brown's estimate we generalise his result quite extensively.Comment: 34 page