Geodesic
Vinogradov’s mean value theorem via efficient congruencing
Trevor D. Wooley1
1 School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom
Annals of mathematics, Tome 175 (2012) no. 3, pp. 1575-1627.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We obtain estimates for Vinogradov’s integral that for the first time approach those conjectured to be the best possible. Several applications of these new bounds are provided. In particular, the conjectured asymptotic formula in Waring’s problem holds for sums of $s$ $k$th powers of natural numbers whenever $s\ge 2k^2+2k-3$.
DOI : 10.4007/annals.2012.175.3.12

Trevor D. Wooley 1

1 School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom 
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Trevor D. Wooley. Vinogradov’s mean value theorem via efficient congruencing. Annals of mathematics, Tome 175 (2012) no. 3, pp. 1575-1627. doi : 10.4007/annals.2012.175.3.12. http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.175.3.12/

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