Min Ru, University of Houston, USA

On M-large divisors and their geometric and arithmetic properties

 

Abstract

Motivated by the classical Theorems of Picard and Siegel and their generalizations, we define the notion of an (essentially) M-large divisor for M > 0 (after Aaron Levin, Heier-Ru) and derive a "master" quantitative-type theorem (in the spirit of Nevanlinna-Schmidt).  As consequences of this "master" theorem, we recover the recent results obtained in this direction (by Corvaja-Zannier, Evertse-Ferretti, Aaron Levin, and Ru, etc.), as well as derive some new results. The master theorem unifies the statements as well as the proofs in this direction.