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On the Waring–Goldbach Problem: Exceptional Sets for Sums of Cubes and Higher Powers

Published online by Cambridge University Press:  20 November 2018

Angel V. Kumchev
Angel V. Kumchev*
Affiliation:
Department of Mathematics, The University of Texas at Austin, 1 University Station C1200, Austin, TX 78712, U.S.A., e-mail: kumchev@math.utexas.edu
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Abstract

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We investigate exceptional sets in the Waring–Goldbach problem. For example, in the cubic case, we show that all but $O\left( {{N}^{79/84+\in }} \right)$ integers subject to the necessary local conditions can be represented as the sum of five cubes of primes. Furthermore, we develop a new device that leads easily to similar estimates for exceptional sets for sums of fourth and higher powers of primes.

Keywords

11P3211L1511L2011N3611P55
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 57 , Issue 2 , 01 April 2005 , pp. 298 - 327
Copyright
Copyright © Canadian Mathematical Society 2005

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