Some Additive Combinatorics Problems in Matrix Rings
Ron Ferguson, Corneliu Hoffman, Florian Luca, Alina Ostafe, Igor, Shparlinski
TL;DR
This paper investigates the distribution of singular and unimodular matrices within sumsets over finite fields and applies these findings to estimate the largest prime divisor of determinants in matrix sumsets over integers.
Contribution
It introduces new results on the distribution of matrices in sumsets over finite fields and connects these to prime divisor estimates over integers.
Findings
Distribution of singular and unimodular matrices characterized
Estimates for the largest prime divisor of determinants obtained
Results applicable to matrix sumsets over finite fields and integers
Abstract
We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite fields. We apply these results to estimate the largest prime divisor of the determinants in sumsets in matrix rings over the integers.
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Taxonomy
TopicsCoding theory and cryptography · Analytic Number Theory Research · Finite Group Theory Research