On the density of rectangular unimodular matrices over the algebraic integers

Vortrag von Dr. Violetta Weger

Datum: 06.06.18  Zeit: 16.00 - 17.00  Raum:

A very well known result in the area of densities is the Mertens-Cesáro Theorem, which states that the density of coprime pairs of Z is 1/zeta(2), where zeta denotes the Riemann zeta function. This can be generalized to coprime m-tuples having the density 1/zeta(m).
In this talk we compute the density of nxm rectangular unimodular matrices over the ring of algebraic integers of a number field K. Observe that this result generalizes the Mertens-Cesáro Theorem in two ways: on one hand by looking at rectangular matrices, which are matrices that can be extended to invertible matrices and on the other hand we deal with the more general setting of algebraic integers.
For K=Q, this fixes a proof by Maze, Rosenthal and Wagner. This is joint work with Giacomo Micheli.