Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Yingkun Li
Affiliation:

Technical University of Darmstadt
Date:

Tue, 2017-11-21 11:10 - 12:00 By the classical theory of complex multiplication, the Klein $j$-invariant takes algebraic

values at CM points. In their seminal work on singular moduli, Gross and Zagier gave a

factorization of the difference between two such values, which can be viewed as the exponential

of a special value of a Green's function on the upper half plane. From numerical computations,

they conjectured that the special values of certain higher Green's functions also enjoy similar

algebraicity property. We will revisit this conjecture and discuss some recent progress.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/7600