Exceptional sets in Waring-Goldbach problem for fifth powers

Abstract

We consider exceptional sets in the Waring-Goldbach problem for fifth powers. For example, we prove that all but O(N^131/132) 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

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