p-adic Aspects of Jacobi Forms

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منابع مشابه

p-adic aspects of Jacobi forms

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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An Approach to the p - adic Theory of Jacobi Forms

The theory of p-adic modular forms was developed by J.-P. Serre [8] and N. Katz [5]. This theory is by now considered classical. Investigation of p-adic congruences for modular forms of half-integer weight was carried out by N. Koblitz [6] and led him to deep conjectures. It seems natural to search for p-adic properties of other types of automorphic forms. In this paper we use the Serre approac...

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JACOBI FORMS AND A TWO-VARIABLE p-ADIC L-FUNCTION

Introduction. Consider a Jacobi form φ(τ, z) = ∑ n,r c(n, r)q ζ whose Fourier coefficients c(n, r) are algebraic numbers. Let p be an odd prime. In this paper we associate to φ a Λ-adic p-ordinary form in the sense of [4]. The construction comes from the map Dν introduced in [2], Theorem 3.1. This map associates to a Jacobi form a family of modular forms parametrised by ν. We obtain the two-var...

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ژورنال

عنوان ژورنال: Journal of Number Theory

سال: 1997

ISSN: 0022-314X

DOI: 10.1006/jnth.1997.2095