RESEARCH ARTICLE

Exceptional sets in Waring-Goldbach problem for fifth powers

  • Zhenzhen FENG 1 ,
  • Zhixin LIU , 2
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  • 1. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China
  • 2. School of Mathematics, Tianjin University, Tianjin 300072, China

Received date: 27 Feb 2020

Accepted date: 31 Dec 2020

Published date: 15 Feb 2021

Copyright

2021 Higher Education Press

Abstract

We consider exceptional sets in the Waring-Goldbach problem for fifth powers. For example, we prove that all but O(N131/132) integers satisfying the necessary local conditions can be represented as the sum of 11 fifth powers of primes, which improves the previous results due to A. V. Kumchev [Canad. J. Math., 2005, 57: 298–327] and Z. X. Liu [Int. J. Number Theory, 2012, 8: 1247–1256].

Cite this article

Zhenzhen FENG , Zhixin LIU . Exceptional sets in Waring-Goldbach problem for fifth powers[J]. Frontiers of Mathematics in China, 2021 , 16(1) : 49 -58 . DOI: 10.1007/s11464-021-0899-4

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