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arXiv · 2603.00660

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

Meng Gao·Jinjiang Li·Linji Long·Min Zhang
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Abstract

In this paper, it is proved that, for any $\gamma_1,\gamma_2,\gamma_3,\gamma_4,\gamma_5\in(\frac{28}{29},1)$, 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 $p_i=\lfloor m_i^{1/\gamma_i}\rfloor$ 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].

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Meng Gao, Jinjiang Li, Linji Long, Min Zhang. 2026-02-28. On the quadratic Waring-Goldbach problem with primes in Piatetski-Shapiro sets. https://arxiv.org/abs/2603.00660

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