On unitals with many Baer sublines

We identify the points of PG(2, q) with the directions of lines in GF(q(3)) , viewed as a 3-dimensional affine space over GF(q). Within this frameork w e associate to a unital in GF(2, q) a certain polynomial in to variables, a nd show that the combinatorial properties of the unital force certain restr ictions on the coefficients of this polynomial. In particular, if q = p(2) here p is prime then e show that a unital is classical if and only if at le ast (q - 2)root q secant lines meet it in the points of a Baer subline.