@article{Luo2025, 
author = {Yifan Luo and Kaisheng Lei and Qingzhong Ji},
title = {On the sumsets of units in a ring of matrices over        Z        /    m      Z},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {3},
pages = {1323-1332},
keywords = {rings of matrices, finite fields, sums of units, Fourier transformation},
url = {https://www.sciopen.com/article/10.3934/era.2025059},
doi = {10.3934/era.2025059},
abstract = {Let        M          n      ,      m        :=  M  a      t    n    (      Z        /    m      Z    ) be the ring of matrices of    n  ×  n over        Z        /    m      Z   and        G          n      ,      m        :=  G      l    n    (      Z        /    m      Z    ) be the multiplicative group of units of        M          n      ,      m       with    n  ⩾  2  ,  m  ⩾  2. In this paper, we obtain an exact formula for the number of representations of any element of        M          2      ,      m       as the sum of    k units in        M          2      ,      m      . Furthermore, by using the technique of Fourier transformation, we also give a formula for the case    n  ≥  3 and    m  =  p is a prime.}
}