The image and kernel of Atkin’s $U_{p}$ operator modulo $p$
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- by Michael Dewar PDF
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Abstract:
We compute the image of Atkin’s $U_{p}$ operator on reduced modular forms. If $A\geq 1$ and $2\leq B \leq p+1$, then $U_{p}: \widetilde M_{Ap+B}\left ( \Gamma _{1}(N) \right ) \twoheadrightarrow \widetilde M_{A+B} \left (\Gamma _{1}(N) \right )$ is a surjection. In particular, the dimension of $\ker U_{p}$ is known for weights at least $p+2$.References
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Additional Information
- Michael Dewar
- Affiliation: Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario K7L 3N6, Canada
- Received by editor(s): February 9, 2011
- Published electronically: October 14, 2011
- Communicated by: Matthew A. Papanikolas
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 1931-1938
- MSC (2010): Primary 11F11, 11F33
- DOI: https://doi.org/10.1090/S0002-9939-2011-11115-8
- MathSciNet review: 2888180