Another proof of Stoll's theorem for moving targets
Seiki Mori · Tohoku Mathematical Journal · 1989
In 1929, Nevanlinna [5] asked whether his defect relation remains valid for mutually distinct meromorphic target functions g ί9 , g q on C which grow more slowly than a given meromorphic function / on C, that is, the Nevanlinna characteristic functions of those functions satisfyNevanlinna [5] proved the conjecture for q = 3. Dufresnoy [3] proved a defect relation with defect bound d+2 for polynomials of degree ^d as target functions.Chuang [2] obtained a defect relation with bound p(l-δ f (oo))+l for slow moving target functions which span a vector space of dimension p over C. Thus Nevanlinna's conjecture is valid for an entire function / on C. In 1986, Steinmetz [8] proved Nevanlinna's conjecture with an elegant short proof.On the other hand, in higher dimension, Shiftman [6], [7] proved Nevanlinna's conjecture for a meromorphic function / on C n if (*) rank{{/} u Φ} = 1 + rank Φ ,