Arithmetic formulas for the Fourier coefficients of Hauptmoduln of level 2, 3, and 5

Matsusaka, Toshiki; Osanai, Ryotaro

doi:10.1090/proc/13333

Arithmetic formulas for the Fourier coefficients of Hauptmoduln of level 2, 3, and 5
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by Toshiki Matsusaka and Ryotaro Osanai PDF

Proc. Amer. Math. Soc. 145 (2017), 1383-1392 Request permission

Abstract:

We give arithmetic formulas for the coefficients of Hauptmoduln of higher level as analogues of Kaneko’s formula for the $j$-invariant. We also obtain their asymptotic formulas by employing Murty-Sampath’s method.

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