Universiteit Leiden Mathematisch Instituut
Geometry Seminar

Tuesday, 5 May 2009, 15:00–16:00, Sn401

Ted Chinburg: Recognizing zeta functions from unit groups

Abstract:

Suppose K is a totally real number field and that O_K^* is the group of units of the integers of K. Let QL_K be the rational vector space spanned by the image of O_K^* under the usual log embedding into R^{r(K)}, where r(K) is the number of archimdean places of K. The Euclidean metric on $R^{r(K)}$ makes QL_K into a metric space. I will sketch a proof that the isometry class of QL_K determines the zeta function $\zeta_K(s)$ when one assumes Schanuel's conjecture; this is joint work with C. Rajan.