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Not for further distribution unless allowed by the License or with the express written permission of Cambridge University Press.
https://doi.org/10.1112/S0025579317000134
Chalmers Tekniska Högskola
Downloaded from https://www.cambridge.org/core. Chalmers Tekniska Högskola, on 09 Mar 2018 at 12:48:23, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms.
2018-03-09T12:48:23+00:00
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/Author(Brandes, J., Wooley, T.)
/Title(Vinogradov systems with a slice off)
/Subject(Let I-s,I-k,I-r\(X\) denote the number of integral solutions of the modified Vinogradov system of equations with 1 <= x\(i\),y\(i\) <= X \(1 <= i <= s\). By exploiting sharp estimates for an auxiliary mean value, we obtain bounds for I-s,I-k,I-r\(X\) for 1 <= r <= k - 1. In particular, when s,k is an element of N satisfy k >= 3 and 1 <= s <= \(k\(2\) - 1\)/2, we establish the essentially diagonal behaviour I-s,I-k,I-l\(X\) << Xs+epsilon.)
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