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The Fourier Coefficients of the ModularFunction λ(τ)

Published online by Cambridge University Press:  20 November 2018

William H. Simons
William H. Simons*
Affiliation:
The University of British Columbia
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In [3], H. Rademacher obtained a convergent series for the Fourier coefficients of the modular invariant J(τ). He found that in the expansion

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 4 , 1952 , pp. 67 - 80
Copyright
Copyright © Canadian Mathematical Society 1952

References

1. Davenport, H.,On certain exponential sums, J. Reine Angew. Math., Bd. 169 (1933), 158–176.Google Scholar
2. Estermann, T., Vereinfachter Beweis ein.es Satz von Kloosterman, Abhandlungen aus dem Mathematischen Seminar der Hamburgischen Universität, Bd. 7 (1939), 82-98, especially 94.Google Scholar
3. Rademacher, H., The Fourier coefficients of the modular invariant J(T), Amer. J. Math., vol. 60 (1938), 501–512.Google Scholar
4. Salie, H., Zur Abschatzung der Fourierkoeffizienten ganzer Modulformen, Math. Z., Bd. 36 (1933), 263–278.Google Scholar
5. Tannery, J. and Molk, J., Théorie des fonctions elliptiques, Tome II (Paris, 1896), 290.Google Scholar
6. Watson, G. N., Theory of Bessel functions (Cambridge, 1922), 181.Google Scholar