Sebastián Herrero: Special values of Green’s functions on hyperbolic 3-space

Speaker
Sebastián Herrero, ETH Zürich and University of Santiago de Chile

Abstract
In 1986 Gross and Zagier stated an algebraicity conjecture for special values of higher Green’s functions on modular curves, which resembles the properties of the modular j function in the theory of complex multiplication. This conjecture has recently been demonstrated by Bruinier, Li and Yang. In this talk I will present new results on an analogous problem for special values of Green’s functions on hyperbolic 3-space. We prove that their averages can be computed in terms of logarithms of primes and logarithms of units in real quadratic fields. This is work in collaboration with Özlem Imamoglu, Anna von Pippich and Markus Schwagenscheidt.