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

Posted in

- Talk [1]

Speaker:

Toshiki Matsusaka
Affiliation:

Kyushu University
Date:

Mon, 2017-11-20 16:30 - 17:10 By the work of R. Borcherds we know the Fourier coefficients of the elliptic modular $j$-function are closely related

to the Monster group. As a new perspective, M. Kaneko gave an arithmetic formula for the Fourier coefficients expressed

in terms of the traces of the CM values of the $j$-function in 1996. In this talk, we consider analogues of this formula for

the McKay-Thompson series. Our main result is an explicit formula for the coefficients expressed in terms of the CM

values of certain hauptmoduln. Furthermore, we give some applications.

**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