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- Title
Spectral Expansions of Overconvergent Modular Functions.
- Authors
Loeffler, David
- Abstract
The main result of this article is an instance of the conjecture made by Gouvêa and Mazur in [11], which asserts that for certain values of r the space of r-overconvergent p-adic modular forms of tame level N and weight k should be spanned by the finite slope Hecke eigenforms. For N = 1, p = 2 and k = 0 we show that this follows from the combinatorial approach initiated by Emerton [9] and Smithline [16], using the classical LU decomposition and results of Buzzard–Calegari [1]; this implies the conjecture for all r∈(512,712). Similar results follow for p = 3 and p = 5 with the assumption of a plausible conjecture, which would also imply formulae for the slopes analogous to those of [1].
- Subjects
MODULAR functions; ELLIPTIC functions; HECKE algebras; MATHEMATICAL formulas; MATHEMATICAL analysis
- Publication
IMRN: International Mathematics Research Notices, 2007, Vol 2007, p1
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnm050