In this paper, Mahler investigates the question whether automorphic functions of Fuchsian type can satisfy algebraic differential equations of the second order. Under rather general restrictions on the corresponding group, it is proved that there is no such differential equation.
Reprint of the author's paper [J. Aust. Math. Soc. 10, 445--450 (1969; Zbl 0207.08302)].