Frontiers of Mathematics in China >
Exceptional sets in Waring-Goldbach problem for fifth powers
Received date: 27 Feb 2020
Accepted date: 31 Dec 2020
Published date: 15 Feb 2021
Copyright
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].
Key words: Exceptional sets; Waring-Goldbach problem; circle method
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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