منابع مشابه
Nearly 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.
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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 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.
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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: Annales de l’institut Fourier
سال: 2013
ISSN: 0373-0956,1777-5310
DOI: 10.5802/aif.2759