A Characterization of T_(2g+1,2) among Alternating Knots

Let K be a genus g alternating knot with Alexander polynomial Δ_K(T) = ∑^g_i = _(−g)a_iT^. We show that if |a_g| = |a_(g−1)|, then K is the torus knot T_(2g+1,±2). This is a special case of the Fox Trapezoidal Conjecture. The proof uses Ozsváth and Szabó's work on alternating knots.