Geodesic
Slim Exceptional Sets for Sums of Cubes
Canadian journal of mathematics, Tome 54 (2002) no. 2, pp. 417-448

Voir la notice de l'article provenant de la source Cambridge University Press

We investigate exceptional sets associated with various additive problems involving sums of cubes. By developing a method wherein an exponential sum over the set of exceptions is employed explicitly within the Hardy-Littlewood method, we are better able to exploit excess variables. By way of illustration, we show that the number of odd integers not divisible by 9, and not exceeding $X$ , that fail to have a representation as the sum of 7 cubes of prime numbers, is $O\left( {{X}^{23/36+\varepsilon }} \right)$ . For sums of eight cubes of prime numbers, the corresponding number of exceptional integers is $O\left( {{X}^{11/36+\varepsilon }} \right)$ .
DOI : 10.4153/CJM-2002-014-4
Mots-clés : 11P32, 11P05, 11P55, Waring’s problem, exceptional sets 
Wooley, Trevor D. Slim Exceptional Sets for Sums of Cubes. Canadian journal of mathematics, Tome 54 (2002) no. 2, pp. 417-448. doi: 10.4153/CJM-2002-014-4
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