Binary linear forms as sums of two squares

Binary linear forms as sums of two squares

We revisit recent work of Heath-Brown on the average order of the quantity r(L1(x))⋯r(L4(x)), for suitable binary linear forms L1,…,L4, as x=(x1,x2) ranges over quite general regions in ℤ2. In addition to improving the error term in Heath-Brown’s estimate, we generalise his result to cover a wider c...

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Veröffentlicht in:Compositio mathematica 2008-11, Vol.144 (6), p.1375-1402
Hauptverfasser: de la Bretèche, R., Browning, T. D.
Format: Artikel
Sprache:eng
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Zusammenfassung:We revisit recent work of Heath-Brown on the average order of the quantity r(L1(x))⋯r(L4(x)), for suitable binary linear forms L1,…,L4, as x=(x1,x2) ranges over quite general regions in ℤ2. In addition to improving the error term in Heath-Brown’s estimate, we generalise his result to cover a wider class of linear forms.
ISSN:0010-437X
1570-5846
DOI:10.1112/S0010437X08003692