Reprint: On algebraic differential equations satisfied by automorphic functions (1969)
Doc. Math. Extra Vol. Mahler Selecta, 661-667 (2019)
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. \par Reprint of the author's paper [J. Aust. Math. Soc. 10, 445--450 (1969; Zbl 0207.08302)].
Mathematics Subject Classification
11-03, 11F03, 30F35, 34M15