The exceptional set for integers of the form $[(p_1)^c] + [(p_2)^c]$

Roger Baker

The exceptional set for integers of the form $[(p_1)^c] + [(p_2)^c]$

Number Theory 2021-11-19 v1

Authors: Roger Baker

Abstract

Let $1 < c < 24/19$ . We show that the number of integers $n \le N$ that cannot be written as $[p_1^c] + [p_2^c]$ ( $p_1$ , $p_2$ primes) is $O(N^{1-\sigma+\varepsilon})$ . Here $\sigma$ is a positive function of $c$ (given explicitly) and $\varepsilon$ is an arbitrary positive number.

Keywords

exceptional set prime numbers asymptotic estimate integer representation

Cite

@article{arxiv.2111.09869,
  title  = {The exceptional set for integers of the form $[(p_1)^c] + [(p_2)^c]$},
  author = {Roger Baker},
  journal= {arXiv preprint arXiv:2111.09869},
  year   = {2021}
}

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