THE EXCEPTIONAL SET OF ONE PRIME SQUARE AND FIVE PRIME CUBES

For a natural number n, let R(n) denote the number of representations of n as the sum of one square and five cubes of primes. In this paper, it is proved that the anticipated asymptotic formula for R(n) fails for at most $O(N^{{\frac{4}{9}+{\varepsilon}})$ positive integers not exceeding N.

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Bibliographic Details
Published inJournal of the Korean Mathematical Society Vol. 59; no. 3; pp. 439 - 448
Main Author Liu, Yuhui
Format Journal Article
LanguageKorean
Published 2022
Subjects
exceptional set
Waring-Goldbach problem
Hardy-Littlewood method
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Summary:For a natural number n, let R(n) denote the number of representations of n as the sum of one square and five cubes of primes. In this paper, it is proved that the anticipated asymptotic formula for R(n) fails for at most $O(N^{{\frac{4}{9}+{\varepsilon}})$ positive integers not exceeding N.
Bibliography:KISTI1.1003/JNL.JAKO202213341894568
ISSN:0304-9914