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


Authors: Toshiki Matsusaka and Ryotaro Osanai
Journal: Proc. Amer. Math. Soc. 145 (2017), 1383-1392
MSC (2010): Primary 11F03, 11F30
DOI: https://doi.org/10.1090/proc/13333
Published electronically: December 27, 2016
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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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Toshiki Matsusaka
Affiliation: Faculty of Mathematics, Kyushu University, 744 Motooka Nishi - ku, Fukuoka, Japan
Email: toshikimatsusaka@gmail.com

Ryotaro Osanai
Affiliation: Faculty of Mathematics, Kyushu University, 744 Motooka Nishi - ku, Fukuoka, Japan
Email: ryotaroosanai@gmail.com

DOI: https://doi.org/10.1090/proc/13333
Received by editor(s): February 21, 2016
Received by editor(s) in revised form: May 15, 2016
Published electronically: December 27, 2016
Communicated by: Kathrin Bringmann
Article copyright: © Copyright 2016 American Mathematical Society