#### 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

#### Recommended Citation

Toropu, Cristina. "ABC THEOREMS IN THE FUNCTIONAL CASE." (2014). http://digitalrepository.unm.edu/math_etds/49