Number Theory Seminar
The elliptic Zagier conjecture in the CM case
Speaker: Diego Chicharro Gordo (King`s College London)Date: Friday, 10 January 2025 - 11:30Place: Aula Naranja, ICMAT
Abstract:
The Beilinson conjectures predict that the special values of motivic L-functions can be described, up to some rational factor, in terms of a regulator that is difficult to describe in general. In some simple cases, however, there are explicit descriptions in terms of polylogarithmic functions. For example, the special value s=2 of the Dedekind zeta function of a number field can be written in terms of special values of the Bloch-Wigner dilogarithm, and a precise generalisation of this to other special values was conjectured by Zagier. In this talk, we’ll see a formulation of Zagier’s conjecture for the L-function of symmetric powers of elliptic curves, and sketch how to prove it when the curve has complex multiplication.
