Shabnam Akhtari

Let $K$ be an algebraic number field. The Primitive Element Theorem implies that the number field $K$ can be generated over the field of rational numbers by a single element of $K$. We call such an element a generator of $K$. A simple and natural...

Let F(x, y) be a binary form of degree at least 3 which is irreducible over the rationals. For any fixed non-zero integer m, Thue showed that the equation F(x, y) =m has at most finitely many solutions in integers x, y. I will discuss some...

In order to study interesting arithmetic, algebraic, analytic and geometric properties of binary forms, we often need a way to order them. I will discuss some natural ways to order binary forms F(x , y) with integer coefficients, especially those of...