Diophantine properties for the special values of Dedekind zeta functions

Abstract: According to Nothcott's theorem, any set of algebraic numbers of bounded height and bounded degree is finite. Analogous finiteness properties are also satisfied by many other heights, such as the Faltings height. Given the many conjectural links between heights and special values of L-functions (with the BSD conjecture as the most remarkable example), it is natural to ask whether special values of L-functions satisfy a similar Northcott property. In this talk, we will outline joint work in progress with Fabien Pazuki and Riccardo Pengo that shows the Northcott property does not hold for the Dedekind zeta function at 1/2.

algebraic geometrynumber theory

Audience: researchers in the topic

Boston University Number Theory Seminar