On Dirichlet’s Unit Theorem and the Class Group

So today, I’m going to write about something I’ve learnt that I think is really cool. Unsurprisingly, it’s related to the Class Group; I will get back to my set of posts on Baker’s Theorem and the Class Number Problem, think of this as a nice excursion. I might go quite fast over the basicsContinue reading “On Dirichlet’s Unit Theorem and the Class Group”

Baker’s Theorem and the Class Number Problem (Part 2)

Disclaimer: This post is the second of a set of three(ish) about Baker’s Theorem and the Class Number Problem. It is intended to be informative and not too rigorous. Find part one here! In this post, I’ll introduce the Class Number Problem, before (eventually) pulling these posts together and seeing how Baker’s Theorem is relevantContinue reading “Baker’s Theorem and the Class Number Problem (Part 2)”

Baker’s Theorem and the Class Number Problem (Part 1)

Disclaimer: This post is the first of a set of three(ish) about Baker’s Theorem and the Class Number Problem. It is intended to be informative and not too rigorous. Over roughly 3 posts, I aim to introduce Baker’s Theorem, the Class Number Problem, and then discuss how Baker’s methods solved part of the problem. InContinue reading “Baker’s Theorem and the Class Number Problem (Part 1)”

A Discussion on (Non-)Unique Factorisation

Disclaimer: This post is a quick discussion of some number theory related things; it is not meant to be rigorous. Throughout, I take to be a base field and to be an extension of ; towards the end of the post will represent the Hilbert Class Field of . Recently, I’ve spent a lot ofContinue reading “A Discussion on (Non-)Unique Factorisation”