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

      YUHUI LIU

      Research Article Volume 130 Published: 10 January 2020 Article ID 0008

    • Fulltext

       

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      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

       
      Published
      10 January 2020
      Manuscript received
      11 October 2018
      Manuscript revised
      6 August 2019
      Accepted
      9 August 2019
      Early published
      Unedited version published online
      Final version published online
      9 January 2020

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      Posted on July 25, 2019

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