• Exceptional set in Waring–Goldbach problem: Two squares, two cubes and two sixth powers

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/130/0008

• # Keywords

Waring–Goldbach problem; exceptional set; Hardy–Littlewood method

• # Abstract

Let $R(n)$ denote the number of representations of an even integer $n$ as thesum of two squares, two cubes and two sixth powers of primes, and by $\mathcal{E}(N)$ we denote the number of even integers $n \leq N$ such that the expected asymptotic formula for $R(n)$ fails to hold. In this paper, it is proved that $\mathcal{E}(N) \ll N^{\frac{127}{288}+\varepsilon}$ for any $\varepsilon$ > 0.

• # Author Affiliations

1. School of Mathematical Sciences, Tongji University, Shanghai 200092, People’s Republic of China

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019