On the solutions of S-unit equations and their applications
Organizers
Speaker
Satyabrat Sahoo
Time
Thursday, March 20, 2025 12:15 PM - 1:00 PM
Venue
A4-1
Abstract
Let $F$ be a number field, and let $S$ be a finite set of prime ideals of $F$. In this talk, we will discuss the solutions to the $S$-unit equation $x+y=1$, where $x$ and $y$ are $S$-units. Additionally, we will provide various applications of this discussion. For instance, when $S$ consists of all prime ideals of $F$ that lie above $2$, we will explore the relationship between the solutions of the $S$-unit equation and the solutions of the Fermat equation $x^p+y^p=z^p$ over $F$.