Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

, Volume 79, Issue 2, pp 165–187

Jacobi and Kummer’s ideal numbers

Article

DOI: 10.1007/s12188-009-0020-5

Cite this article as:
Lemmermeyer, F. Abh. Math. Semin. Univ. Hambg. (2009) 79: 165. doi:10.1007/s12188-009-0020-5

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

JacobiKummerDedekindIdeal primesCyclotomic fieldsFermat’s last theoremValuationsIntegral closure

Mathematics Subject Classification (2000)

01A5511R18

Copyright information

© Mathematisches Seminar der Universität Hamburg and Springer 2009

Authors and Affiliations

  1. 1.JagstzellGermany