PreprintCC BY 4.0arXiv
Matrix Waring Problem-III
Abstract
Let n,k be positive integers and q be a prime power. We prove that there exists a real constant Ck depending only on k such that if $ \# M_n(\mathbb{F}_q) > C_k$ then every element in Mn(𝔽q) is a sum of two kth powers, proving Larsen's conjecture.
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BibTeX
@misc{kishore2026matrix,
title = {{Matrix Waring Problem-III}},
author = {Krishna Kishore and Sunil Kumar Mallick},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17698},
eprint = {2610.17698},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17698},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Matrix Waring Problem-III
AU - Krishna Kishore
AU - Sunil Kumar Mallick
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.17698
UR - https://arxiv.org/abs/2610.17698
AB - 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(𝔽_q) is a sum of two kth powers, proving Larsen's conjecture.
ER -