Links to Marc Conrad's papers related to cyclotomic units:

• Conrad, M., Replogle D., Nontrivial Galois Module Structure of Cyclotomic Fields, Mathematics of Computation 72, 891-899, 2003. [link]
• Conrad, M., Construction of Bases for the Group of Cyclotomic Units, Journal of Number Theory 81, 1-15, 2000. [link]
• Conrad, M., On explicit Relations between Cyclotomic Numbers, Acta Arithmetica XCIII.1, 67-76, 2000. [link]
• Conrad, M., About the Kernel of the Augmentation of finitely generated Z-modules, Mathematical Communications 5, 61-66, 2000. [link]

Talks

• Talk at the Mathematical Colloquium in Osijek, 2016. (abstract)
• Announcement of a talk in Exeter, 2004.
• Talk in the Dagstuhl Seminar 'Algorithmen und Zahlentheorie, 1998.

Diploma and PhD thesis (these links are in German)

• Basen von Moduln mit Anwendung auf Kreiseinheiten und Stickelbergerelemente (PhD Thesis) ,
• Diploma thesis

Examples of bases of cyclotomic units and basis representations of generators

• Absolute: n=9, n=12, n=13, n=14, n=15, n=16, n=60, n=81, n=105, n=420.
• Relative: n=9, n=12, n=13, n=14, n=15, n=16, n=60, n=81, n=105, n=420.

Calculate a Basis of the Cyclotomic Units

Choose a number: To keep server load low this interface is restricted to n < 600. Please contact me if you need the algorithm for larger n.
I want to know: a basis ; a table ; a list ; methods (leave all boxes checked for small values)

Relative cyclotomic units only: ;

External Links

(including links citing some of this above; please notify me to include your work here)

• Wikipedia on Cyclotomic Units
• The Artin Defect in Algebraic K-Theory by Dimitrios Patronas, 2014.
• A Note On Ennola Relation by Jae Moon Kim and Jado Ryu, 2014.
• Class Numbers of Real Cyclotomic Fields of Conductor pq by Eleni Agahtocleous, 2009.

---

© by: Marc Conrad, 2004-2016. If you want me to come to your organisation and talk about cyclotomic units please contact me. The material on this page is presented "as is". There is no warranty implied by presenting this stuff. Feel free to use and modify the material for your own teaching. When doing so please link to this web site (http://perisic.com/cyclotomic). In acadmic publications cite this page as: Conrad, Marc (2016) Cyclotomic Units - Relations and Computations (online), available at: http://perisic.com/cyclotomic. The webspace for this project is kindly provided by the Perisic Guesthouse (www.perisic.com).