Fourier coefficients and singular moduli of modular functions

Speaker:

Masanobu Kaneko

Affiliation:

Kyushu University

Date:

Tue, 23/05/2017 - 09:00 - 09:50

Location:

MPIM Lecture Hall [2]

Parent event:

Conference "Modular forms are everywhere" [3]

The generating function of traces of singular moduli of the modular j-invariant
becomes a modular form of weight 3/2. This is Don's celebrated discovery, inspired
by a work of R. Borcherds. Using this modular form, one can obtain a formula for
the Fourier coefficients of the modular j-invariant in terms of singular moduli.
In this talk, I shall review these works, and introduce recent developments
regarding an application of the formula (due to R. Murty and K. Sampath)
as well as generalizations (due to T. Matsusaka).