Work

Waring problem for matrices over finite fields

Year: 2024

Type: article

Abstract: We prove that for all integers k ≥ 1 , q ≥ ( k − 1 ) 4 + 6 k , and m ≥ 1 , every matrix in M m ( F q ) is a sum of two kth powers: M m ( F q ) = { A k + B k | A , B ∈ M m ( F q ) } . We further generalize and refine this result in the cases when both B and C can be chosen to be invertible, cyclic, or split semisimple, when k is coprime to p , or when m is sufficiently large. We also give a criterion for the Waring problem in terms of stabilizers .

Source: Journal of Pure and Applied Algebra

DOI: 10.1016/j.jpaa.2024.107656

Authors: Krishna Kishore, Adrian Vasiu, Sailun Zhan

Institutions: Indian Institute of Technology Tirupati, Binghamton University

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,330

Funder: Science and Engineering Research Board