The factorization of differences of singular moduli is described in a landmark 1985 article
of Gross and Zagier bearing the same title. I will describe a project which aims to uncover similar
phenomena in the setting of real quadratic fields. This is joint work with Jan Vonk.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/7239