Matrix Waring Problem

2021/11/23 by Kishore, Krishna · 1 citation
#11G25 #11P05 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2111.11774

Abstract

We prove that for all integers k ≥ 1, there exists a constant C_k depending only on k, such that for all q > C_k, and for n = 1, 2 every matrix in M_n(\mathbbF_q) is a sum of two kth powers and for all n ≥ 3 every matrix in M_n(\mathbbF_q) is a sum of at most three kth powers.

Cited by

• On sums and products of diagonalizable matrices over division rings

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