Some remarks on cyclic Galois coverings of the projective line over   finite fields
  We study cyclic finite Galois extensions of the rational function field of the projective line P^{1}(F_q) over a finite field F_q with q elements defined by considering quotient curves by finite subgroups of the projective linear group PGL(2,q), and we enumerate them expressing the count in terms of Stirling numbers. 
Alberto Besana, Cristina Martinez Ramirez
math.AG math.GR