منابع مشابه
Classical and overconvergent modular forms
The purpose of this article is to use rigid analysis to clarify the relation between classical modular forms and Katz’s overconvergent forms. In particular, we prove a conjecture of F. Gouvêa [G, Conj. 3] which asserts that every overconvergent p-adic modular form of sufficiently small slope is classical. More precisely, let p > 3 be a prime, K a complete subfield of Cp, N be a positive integer...
متن کاملNearly Overconvergent Modular Forms
We introduce and study finite slope nearly overconvergent (elliptic) modular forms. We give an application of this notion to the construction of the RankinSelberg p-adic L-function on the product of two eigencurves.
متن کاملSlopes of overconvergent 2-adic modular forms
We explicitly compute all the slopes of the Hecke operator U2 acting on overconvergent 2-adic level 1 cusp forms of weight 0: the nth slope is 1 + 2v((3n)!/n!), where v denotes the 2-adic valuation. We formulate an explicit conjecture about what these slopes should be for weight k forms.
متن کاملSlopes of 3-adic overconvergent modular forms
If r = 12 and (uij) is the matrix of the U operator in the above basis, then the numbers uij satisfy a recurrence formula: there is a p × p matrix M such that uij = ∑p r,s=1Mrsui−r,j−s. Furthermore, M is skew-upper-triangular and constant on off diagonals; and the coefficients uij satisfy uij = jiuji. The case p = 2 is extensively studied in [BC05]. Here the recurrence relation is simple enough...
متن کاملSlopes of overconvergent 2 - adic modular forms . Kevin Buzzard
Let p be a prime, and let N be a positive integer coprime to p. Let Mk(Γ1(N);Qp) denote the weight k modular forms of level Γ1(N) defined overQp. In recent years, work of Coleman and others (for example [5],[6],[7],[8],[9]) has shown that a very profitable way of studying this finite-dimensional Qp-vector space is to choose a small positive rational number r and then to embed Mk(Γ1(N);Qp) into ...
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ژورنال
عنوان ژورنال: Inventiones Mathematicae
سال: 1996
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s002220050051