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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Parity of the coefficients of Klein's $ j$-function


Author: Claudia Alfes
Journal: Proc. Amer. Math. Soc. 141 (2013), 123-130
MSC (2010): Primary 11F03, 11F30, 11F33
Published electronically: May 14, 2012
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Abstract: Klein's $ j$-function is one of the most fundamental modular functions in number theory. However, not much is known about the parity of its coefficients. It is believed that the odd coefficients are supported on ``one half'' of the arithmetic progression $ n\equiv 7\pmod {8}$. Following a strategy first employed by Ono for the partition function, we use twisted Borcherds products and results on the nilpotency of the Hecke algebra to obtain new results on the distribution of parity for the coefficients of $ j(z)$.


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Additional Information

Claudia Alfes
Affiliation: Fachbereich Mathematik, Technische Universität Darmstadt, Schloßgartenstr. 7, D-64289 Darmstadt, Germany
Email: alfes@mathematik.tu-darmstadt.de

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11502-3
PII: S 0002-9939(2012)11502-3
Received by editor(s): June 10, 2011
Published electronically: May 14, 2012
Additional Notes: The author was supported by the German Academic Exchange Service.
Communicated by: Ken Ono
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.