The genus of maximal function fields over finite fields
It is proved that if there exists a maximal function field of genus \(g\) over the finite field with \(q^2\) elements, then \(g\leq (q-1)^2/4\) or \(g= qr/2\) with \((q-1)/2\leq r\leq q-1\). The authors conjecture that in the second case \(r= (q-1)\). This conjecture has been proved in the affirmative by Fuhrmann and Torres.
scientific article; zbMATH DE number 733203