p-adic families of modular forms and p-adic Abel-Jacobi maps
نویسندگان
چکیده
منابع مشابه
P-adic Banach Spaces and Families of Modular Forms
Let p be a prime, Cp the completion of an algebraic closure of the p-adicnumbers Qp and K a finite extension of Qp contained in Cp. Let v be the valuation on Cp such that v(p) = 1 and let | | be the absolute value on Cp such that |x| = p for x ∈ Cp. Suppose N is a positive integer prime to p. Let X1(Np) denote the modular curve over K which represents elliptic curves with Γ1(Np)-structure and l...
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We are interested in understanding and describing the p-adic properties of Jacobi forms. As opposed to the case of modular forms, not much work has been done in this area. The literature includes [3, 4, 7]. In the first section, we follow Serre’s ideas from his theory of p-adic modular forms. We study Jacobi forms whose Fourier expansions have integral coefficients and look at congruences betwe...
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Let p be prime, N be a positive integer prime to p, and k be an integer. Let Pk(t) be the characteristic series for Atkin’s U operator as an endomorphism of p-adic overconvergent modular forms of tame level N and weight k. Motivated by conjectures of Gouvêa and Mazur, we strengthen a congruence in [W] between coefficients of Pk and Pk′ for k ′ p-adically close to k. For p − 1 | 12, N = 1, k = 0...
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Serre in the 1970s was the first to formalize such a question on the way to constructing p-adic L-functions, by way of developing the notion of a p-adic modular form to be the p-adic limit of some compatible family of q-expansions of classical modular forms. Katz came along fairly soon afterwards and generalized the theory to a much more geometric context, and showed that Serre’s p-adic forms e...
متن کاملMOCK MODULAR FORMS AS p-ADIC MODULAR FORMS
In this paper, we consider the question of correcting mock modular forms in order to obtain p-adic modular forms. In certain cases we show that a mock modular form M is a p-adic modular form. Furthermore, we prove that otherwise the unique correction of M is intimately related to the shadow of M.
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ژورنال
عنوان ژورنال: Annales mathématiques du Québec
سال: 2016
ISSN: 2195-4755,2195-4763
DOI: 10.1007/s40316-016-0060-z