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On Hecke modules generated by eta-products and imaginary quadratic fields


Author: Takeshi Ogasawara
Journal: Proc. Amer. Math. Soc. 145 (2017), 23-37
MSC (2010): Primary 11F20; Secondary 11R29, 11F11
DOI: https://doi.org/10.1090/proc/13186
Published electronically: June 30, 2016
MathSciNet review: 3565357
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Abstract: We study two types of modules over the Hecke algebra generated by eta-products $ \eta (\tau )\eta (N\tau )$ and $ \eta (\tau )^3\eta (\lambda \tau )^3$ respectively. We give dimension formulas for them in terms of the class number of imaginary quadratic field.


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Additional Information

Takeshi Ogasawara
Affiliation: Department of General Education, National Institute of Technology, Oyama College, 771 Nakakuki, Oyama City, Tochigi, 323-0806, Japan
Email: t.ogasawara.4164@gmail.com

DOI: https://doi.org/10.1090/proc/13186
Keywords: Eta-function, class numbers, modular forms
Received by editor(s): March 3, 2016
Published electronically: June 30, 2016
Communicated by: Ken Ono
Article copyright: © Copyright 2016 American Mathematical Society