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Fourier coefficients and singular moduli of modular functions

Posted in
Masanobu Kaneko
Kyushu University
Tue, 2017-05-23 09:00 - 09:50
MPIM Lecture Hall

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).

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