CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

Slim Exceptional Sets for Sums of Cubes

  Published:2002-04-01
 Printed: Apr 2002
  • Trevor D. Wooley
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

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 $O(X^{23/36+\eps})$. For sums of eight cubes of prime numbers, the corresponding number of exceptional integers is $O(X^{11/36+\eps})$.
Keywords: Waring's problem, exceptional sets Waring's problem, exceptional sets
MSC Classifications: 11P32, 11P05, 11P55 show english descriptions Goldbach-type theorems; other additive questions involving primes
Waring's problem and variants
Applications of the Hardy-Littlewood method [See also 11D85]
11P32 - Goldbach-type theorems; other additive questions involving primes
11P05 - Waring's problem and variants
11P55 - Applications of the Hardy-Littlewood method [See also 11D85]
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/