Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

$ 2$-adic properties of modular functions associated to Fermat curves


Author: Matija Kazalicki
Journal: Proc. Amer. Math. Soc. 139 (2011), 4265-4271
MSC (2000): Primary 11F03, 11F30, 11F33
Published electronically: April 29, 2011
MathSciNet review: 2823072
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For an odd integer $ N$, we study the action of Atkin's $ U(2)$-operator on the modular function $ x(\tau)$ associated to the Fermat curve: $ X^N+Y^N=1$. The function $ x(\tau)$ is modular for the Fermat group $ \Phi(N)$, generically a noncongruence subgroup. If $ x(\tau)=q^{-1}+\sum_{i=1}^\infty a(iN-1)q^{iN-1}$, we essentially prove that $ \lim_{n \rightarrow 0}a(n)=0$ in the $ 2$-adic topology.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11F03, 11F30, 11F33

Retrieve articles in all journals with MSC (2000): 11F03, 11F30, 11F33


Additional Information

Matija Kazalicki
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Address at time of publication: Department of Mathematics, University of Zagreb, Bijenicka cesta 30, 10000 Zagreb, Croatia
Email: kazalick@math.wisc.edu, mkazal@math.hr

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10854-2
PII: S 0002-9939(2011)10854-2
Keywords: Modular forms, noncongruence subgroups, Fermat curves
Received by editor(s): April 13, 2010
Received by editor(s) in revised form: September 20, 2010, and October 23, 2010
Published electronically: April 29, 2011
Communicated by: Kathrin Bringmann
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.