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

 

The effective Chebotarev density theorem and modular forms modulo $ \mathfrak{m}$


Author: Sam Lichtenstein
Journal: Proc. Amer. Math. Soc. 136 (2008), 3419-3428
MSC (2000): Primary 11F33
Published electronically: May 7, 2008
MathSciNet review: 2415025
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Abstract: Suppose that $ f$ (resp. $ g$) is a modular form of integral (resp. half-integral) weight with coefficients in the ring of integers $ \mathcal{O}_K$ of a number field $ K$. For any ideal $ \mathfrak{m}\subset \mathcal{O}_K$, we bound the first prime $ p$ for which $ f\mid T_p$ (resp. $ g\mid T_{p^2}$) is zero ( $ \mod\mathfrak{m}$). Applications include the solution to a question of Ono (2001) concerning partitions.


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Additional Information

Sam Lichtenstein
Affiliation: 286 Adams House Mail Center, Harvard University, Cambridge, Massachusetts 02138
Email: sflicht@fas.harvard.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09333-7
PII: S 0002-9939(08)09333-7
Received by editor(s): July 18, 2007
Received by editor(s) in revised form: August 25, 2007
Published electronically: May 7, 2008
Communicated by: Ken Ono
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.