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On the quadratic Waring-Goldbach problem with primes in Piatetski-Shapiro sets

Meng Gao, Jinjiang Li, Linji Long, Min Zhang

Abstract

In this paper, it is proved that, for any $γ_1,γ_2,γ_3,γ_4,γ_5\in(\frac{28}{29},1)$, every sufficiently large integer $n$ subject to $n\equiv5\pmod{24}$ can be represented as the sum of five squares of primes, i.e., \begin{equation*} n=p_1^2+p_2^2+p_3^2+p_4^2+p_5^2, \end{equation*} such that $p_i=\lfloor m_i^{1/γ_i}\rfloor$ for some $m_i\in\mathbb{N}^+$ for each $1\leqslant i\leqslant 5$. This result constitutes an improvement upon the previous result of Zhang and Zhai [29].

On the quadratic Waring-Goldbach problem with primes in Piatetski-Shapiro sets

Abstract

In this paper, it is proved that, for any , every sufficiently large integer subject to can be represented as the sum of five squares of primes, i.e., \begin{equation*} n=p_1^2+p_2^2+p_3^2+p_4^2+p_5^2, \end{equation*} such that for some for each . This result constitutes an improvement upon the previous result of Zhang and Zhai [29].
Paper Structure (4 sections, 58 equations)

This paper contains 4 sections, 58 equations.

Table of Contents

  1. Introduction and main result
  2. Transference principle
  3. Mean value estimate
  4. Proof of Theorem \ref{['Theorem-1']}

Theorems & Definitions (7)

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