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

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      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

       

      YUHUI LIU1

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

       
  • Proceedings – Mathematical Sciences | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2021-2022 Indian Academy of Sciences, Bengaluru.