In the field of arithmetic dynamics, we study number theoretic aspects of discrete dynamical systems induced by rational maps on projective spaces. Among the rational …
This dissertation discusses the ramification-theoretic behavior of Galois representations attached to dynamical systems over local fields, with applications to global fields. These arboreal representations are …
The work in this thesis concerns two problems in arithmetic dynamics: forward orbit problems over finite fields, and inverse image problems over local fields. We …
While the study of algebraic curves and their moduli has been a celebrated subject in algebraic and arithmetic geometry, generalizations of many results that hold …
In this disseration, we generalize the classical result relating special values of the real analytic GL2 Eisenstein series to the product of the Riemann zeta …
In a celebrated paper published in 1983, R. Mañé, P. Sad, and D. Sullivan proved a result about holomorphic families of injections called the λ-Lemma …
In this work we provide a meromorphic continuation in three complex variables of two types of triple shifted convolution sums of Fourier coefficients of holomorphic …
Faltings's theorem states that a smooth geometrically irreducible projective curve of genus at least two defined over a number field has finitely many rational points. …
