A Quadratic Bound for Automorphism Groups of Curves of Positive $p$-Rank in Odd Characteristic

Let $X$ be a nonsingular projective curve of genus $g\ge2$ over an algebraically closed field of odd characteristic $p$. Giulietti and Korchmáros established a quadratic genus bound with constant $900$ forcing zero $p$-rank for curves of even genus. We extend this bound to odd genus: for every $g\ge