Publication Date

7-12-2014

Abstract

In this dissertation we will prove some ABC Theorems, namely for relatively prime by pairs p-adic entire functions in one variable, for p-adic meromorphic functions in several variables without common factors, under the hypothesis that no subsum vanishes, and also for pairwise relatively prime p-adic entire functions of several variables. In this thesis we will also prove a few generalizations of Buium's results that he used in order to prove his ABC Theorems for isotrivial abelian varieties, respectively with trace zero. We hope to be able to use these results in order to prove a version of an ABC Theorem for any abelian variety over a function field.

Degree Name

Mathematics

Level of Degree

Doctoral

Department Name

Mathematics & Statistics

First Advisor

Buium, Alexandr

First Committee Member (Chair)

Boyer, Charles

Second Committee Member

Nakamaye, Michael

Third Committee Member

Heier, Gordon

Language

English

Keywords

ABC THEOREMS

Document Type

Dissertation

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