Sums of eight fourth power of primes

Yang Qu; Rong Ma

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arXiv · 2512.14386

Sums of eight fourth power of primes

Yang Qu·Rong Ma

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Abstract

For any sufficiently large $\ell$, suppose that $\ell$ can be expressed as $$ \ell=p_1^4+p_2^4+p_3^4+ \cdots +p_8^4,$$ where $p_1, p_2,p_3,\cdots, p_8$ are primes.For such $\ell$, in this paper we will use circle method and sieves to prove that the proportion of $\ell$ in positive integers is at least $\frac{1}{414.465}$ .

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Yang Qu, Rong Ma. 2025-12-16. Sums of eight fourth power of primes. https://arxiv.org/abs/2512.14386

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