Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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THE EXCEPTIONAL SET OF ONE PRIME SQUARE AND FIVE PRIME CUBES

  • Liu, Yuhui (School of Science Jiangnan University)
  • Received : 2019.10.06
  • Accepted : 2022.01.19
  • Published : 2022.05.01
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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

Acknowledgement

The author would like to thank the anonymous referee for his/her patience and time in refereeing this manuscript and express the most sincere gratitude to Professor Yingchun Cai for his valuable advice and constant encouragement.

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