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arXiv · 2610.17698

Matrix Waring Problem-III

Krishna Kishore·Sunil Kumar Mallick
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Abstract

Let $n,k$ be positive integers and $q$ be a prime power. We prove that there exists a real constant $C_k$ depending only on $k$ such that if $ \# M_n(\mathbb{F}_q) > C_k$ then every element in $M_n(\mathbb{F}_q)$ is a sum of two $k$th powers, proving Larsen's conjecture.

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Krishna Kishore, Sunil Kumar Mallick. 2026-10-13. Matrix Waring Problem-III. https://arxiv.org/abs/2610.17698

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