Distribution of Determinant of Matrices With Restricted Entries Over Finite Fields (pp. 203-212)
Authors: L.A. Vinh
Abstract: For a prime power q, we study the distribution of determinant of matrices with restricted entries over a finite field F2 of q elements. More precisely, let Nd (A;t) be the number of d×d matrices with entries in A having determinant t. We show that
Nd(A ;t) = (1+o(1)) |A |d2/q,
if |A |=ω(qd/(2d-1)/(2d−1)), d ≥ 4. When q is a prime and A is a symmetric interval [−H,H], we get the same result for d ≥ 3. This improves a result of Ahmadi and Shparlinski (2007).