The Analytic Class Number Formula for Cyclotomic Fields and Fermat’s Last Theorem

Specialeforsvar ved Kenneth Jensen

Titel: The Analytic Class Number Formula for Cyclotomic Fields and Fermat’s Last Theorem

Abstract: In this thesis, we will use the analytic class number formula for prime cyclotomic field to show that for an odd prime the class number of the prime cyclotomic field is a product of two natural numbers, one of which is the class number of the real part of the prime cyclotomic field. We will use this decomposition of the class number to find a criterion for regularity. To do this we will define the Bernoulli numbers and show some properties of them. We also study valuation on a field, and show some statements about them. We will also show Kummer's Lemma and use this to show the second case of Fermat's Theorem for regular odd primes.

Vejleder: Ian Kiming
Censor: Tom Høholdt