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Speaker:

Toshiki Matsusaka
Affiliation:

Kyushu University
Date:

Mon, 2017-11-20 16:30 - 17:10
Location:

MPIM Lecture Hall 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.

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