Visualisierungen des Induktionsprinzips

in Beiträge zum Mathematikunterricht 2020 (2020)

Kummer theory for number fields and the reductions of algebraic numbers

in International Journal of Number Theory (2019)

For all number fields the failure of maximality for the Kummer extensions is bounded in a very strong sense. We give a direct proof (without relying on the Bashmakov-Ribet method) of the fact that if G is ... [more ▼]

For all number fields the failure of maximality for the Kummer extensions is bounded in a very strong sense. We give a direct proof (without relying on the Bashmakov-Ribet method) of the fact that if G is a finitely generated and torsion-free multiplicative subgroup of a number field K having rank r, then the ratio between n^r and the Kummer degree [K(\zeta_n,\sqrt[n]{G}):K(\zeta_n)] is bounded independently of n. We then apply this result to generalise to higher rank a theorem of Ziegler from 2006 about the multiplicative order of the reductions of algebraic integers (the multiplicative order must be in a given arithmetic progression, and an additional Frobenius condition may be considered). [less ▲]

Multisets

Article for general public (2019)

Reductions of points on algebraic groups

in Journal of the Institute of Mathematics of Jussieu (2019)

Reductions of elliptic curves

in Proceedings of the Roman Number Theory Association (2019), 4

Multisets in arithmetics

in Multimengen in der Arithmetik (2019)

Arithmetic billiards

Article for general public (2018)

Math around the Clock

Article for general public (2018)

This is an article for the general public about mathematical clocks. Several original mathematical clocks are also presented.

Driehoeken met onderling 5 gelijke zijden en hoeken

Article for general public (2018)

The 1-eigenspace for matrices in GL2(ℤℓ)

in New York Journal of Mathematics (2017)