Binary linear forms as sums of two squares

Abstract

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.

34 pages

References in corpus (1)

• Sums of arithmetic functions over values of binary forms

Cited by in corpus (5)

• Le problème des diviseurs pour des formes binaires de degré 4
• On Manin's conjecture for a family of Châtelet surfaces
• Sur le nombre d'idéaux dont la norme est la valeur d'une forme binaire de degré 3
• Generalised divisor sums of binary forms over number fields
• Binary forms as sums of two squares and Châtelet surfaces