Overconvergent modular forms and their explicit arithmetic
نویسندگان
چکیده
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...
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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...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 2020
ISSN: 0273-0979,1088-9485
DOI: 10.1090/bull/1700