Picard constants of three-sheeted algebroid surfaces with p(y)=5

Abstract

In 1995 Sawada-Tohge proved that every three-sheeted algebroid Riemann surface with p(y)=5 is of Picard constant 5, unless its discriminant has a form e^δH(Ae^4H+B), where δ=0 or 1. In this paper we shall prove that the result remains valid with no condition.