On GCD Bounds


Julie Tzu-Yueh Wang

11:10:00 - 12:10:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

We will give a brief survey on gcd bounds over number fields, polynomial rings, algebraic function fields and for entire functions. The problem giving upper bounds for the counting function of common zeros (i.e. the gcd) of two entire analytic functions in various settings will then be discussed. Applying techniques from analytic number theory and Diophantine approximation in the context of entire and meromorphic functions, we establish bounds of this type covering several aspects that were not well-suited for the previously used methods in the context of this problem. This is a joint work with Hector Pasten.