On the solutions of S-unit equations and their applications
演讲者
Satyabrat Sahoo
时间
2025年03月20日 12:15 至 13:00
地点
A4-1
摘要
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 $F$.