Talk page

Title:
Oscillations in Mertens’ product theorem for number fields

Speaker:
Ethan Lee

Abstract:
The content of this talk is based on joint work with Shehzad Hathi. First, I will give a short but sweet proof of Mertens’ product theorem for number fields, which generalises a method introduced by Hardy. Next, when the number field is the rationals, we know that the error in this result changes sign infinitely often. Therefore, a natural question to consider is whether this is always the case for any number field? I will answer this question (and more) during the talk. Furthermore, I will present the outcome of some computations in two number fields: $\mathbb{Q}(\sqrt{5})$ and $\mathbb{Q}(\sqrt{13})$.

Link:
https://mathtube.org/lecture/video/oscillations-mertens%E2%80%99-product-theorem-number-fields

Workshop:
Mathtube- Comparative Prime Number Theory