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Speaker:
Toshiki Matsusaka
Affiliation:
Kyushu University
Date:
Mon, 20/11/2017 - 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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