Vinogradov systems with a slice off

Julia Brandes, Trevor D Wooley

Research output: Contribution to journalArticle (Academic Journal)

2 Citations (Scopus)
243 Downloads (Pure)

Abstract

Let Is,k,r(X) denote the number of integral solutions of the modified Vinogradov system of equations xj1+…+xjs=yj1+…+yjs(1≤j≤k, j≠r), with 1≤xi,yi≤X (1≤i≤s). By exploiting sharp estimates for an auxiliary mean value, we obtain bounds for Is,k,r(X) for 1≤r≤k−1. In particular, when s,k∈N satisfy k≥3 and 1≤s≤(k2−1)/2, we establish the essentially diagonal behaviour Is,k,1(X)≪Xs+ϵ.
Original languageEnglish
Pages (from-to)797-817
Number of pages21
JournalMathematika
Volume63
Issue number3
Early online date29 Nov 2017
DOIs
Publication statusPublished - Nov 2017

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