Article

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

, Volume 79, Issue 2, pp 165-187

First online:

Jacobi and Kummer’s ideal numbers

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

In this article we give a modern interpretation of Kummer’s ideal numbers and show how they developed from Jacobi’s work on cyclotomy, in particular the methods for studying “Jacobi sums” which he presented in his lectures on number theory and cyclotomy in the winter semester 1836/37.

Keywords

Jacobi Kummer Dedekind Ideal primes Cyclotomic fields Fermat’s last theorem Valuations Integral closure

Mathematics Subject Classification (2000)

01A55 11R18