On unitals with many Baer sublines (Q1963153)

After identifying points of \(\text{PG}(2,q)\) with the slopes of lines in \(\text{GF}(q^3)\), regarded as a \(3\)-dimensional affine space over the field \(\text{GF}(q)\), the authors associate to a unital \(\mathcal U\) in \(\text{PG}(2,q)\), a polynomial in two variables. They show that the combinatorial properties of \(\mathcal U\) yield some restrictions on the coefficients of the polynomial. Assuming \(q=p^2\), \(p\) a prime, they show that \(\mathcal U\) is classical if and only if it has at least \((q-2)\sqrt q\) Baer subplanes among its secants.