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Oscillations in Mertens’ product theorem for number fields

Speaker: Ethan Lee

Date: Tue, Jun 18, 2024

Location: PIMS, University of British Columbia

Conference: Comparative Prime Number Theory

Subject: Mathematics, Number Theory

Class: Scientific

CRG: L-Functions in Analytic Number Theory

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 $\mathbb{Q}(\sqrt{13})$.