Abstract
Clearly, the only holomorphic eta product of weight k for the full modular group is η 2k(z). Lacunary powers of the eta function have been studied by Serre [Glasgow Math. J. 27, 203–221, 1985] exhaustively. Here we will present theta series representations for some modular forms on the full modular group, including Serre’s results on powers of η(z).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J.-P. Serre, Sur la lacunarité des puissances de η, Glasg. Math. J. 27 (1985), 203–221.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Köhler, G. (2011). Level 1: The Full Modular Group. In: Eta Products and Theta Series Identities. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16152-0_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-16152-0_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16151-3
Online ISBN: 978-3-642-16152-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)