- Acta Math.
- Volume 213, Number 2 (2014), 199-236.
On Vinogradov’s mean value theorem: strongly diagonal behaviour via efficient congruencing
We enhance the efficient congruencing method for estimating Vinogradov’s integral for moments of order 2s, with . In this way, we prove the main conjecture for such even moments when , showing that the moments exhibit strongly diagonal behaviour in this range. There are improvements also for larger values of s, these finding application to the asymptotic formula in Waring’s problem.
The first author was supported in part by National Science Foundation grants DMS-0901339 and DMS-1201442.
The second author was supported in part by a Royal Society Wolfson Research Merit Award.
Acta Math., Volume 213, Number 2 (2014), 199-236.
Received: 25 April 2013
Revised: 5 November 2013
First available in Project Euclid: 30 January 2017
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2014 © Institut Mittag-Leffler
Ford, Kevin; Wooley, Trevor D. On Vinogradov’s mean value theorem: strongly diagonal behaviour via efficient congruencing. Acta Math. 213 (2014), no. 2, 199--236. doi:10.1007/s11511-014-0119-0. https://projecteuclid.org/euclid.acta/1485801866