On some matrix counting problems
Ali Mohammadi, Alina Ostafe, Igor E. Shparlinski · Journal of the London Mathematical Society · 2024
Abstract We estimate the frequency of singular matrices and of matrices of a given rank whose entries are parametrised by arbitrary polynomials over the integers and modulo a prime . In particular, in the integer case, we improve a recent bound of V. Blomer and J. Li (2022).