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Arithmetic formulas for the coefficients of the McKay-Thompson series

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Toshiki Matsusaka
Kyushu University
Mon, 2017-11-20 16:30 - 17:10
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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