Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

HOME ALL ARTICLES View

J. Korean Math. Soc. 2022; 59(3): 439-448

Published online May 1, 2022 https://doi.org/10.4134/JKMS.j190679

Copyright © The Korean Mathematical Society.

The exceptional set of one prime square and five prime cubes

Yuhui Liu

Jiangnan University

Abstract

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 $N$.

Keywords: Waring-Goldbach problem, exceptional set, Hardy-Littlewood method

MSC numbers: 11P05, 11P32

Supported by: Project supported by the National Natural Science Foundation of China (grant no. 11771333) and by the Fundamental Research Funds for the Central Universities (grant no. JUSRP122031).

Stats or Metrics

Share this article on :

Related articles in JKMS

more +