Nearly Overconvergent Modular Forms
نویسنده
چکیده
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.
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 کاملOverconvergent modular symbols Arizona Winter School 2011
Course description: This course will give an introduction to the theory of overconvergent modular symbols. This theory mirrors the theory of overconvergent modular forms in that both spaces encode the same systems of Hecke-eigenvalues. Moreover, the theory of overconvergent modular symbols has the great feature of being easily computable and is intimately connected to the theory of p-adic L-fun...
متن کاملOn the Up operator acting on p-adic overconvergent modular forms when X0(p) has genus 1
In this note we will show how to compute Up acting on spaces of overconvergent p-adic modular forms when X0(p) has genus 1. We first give a construction of Banach bases for spaces of overconvergent p-adic modular forms, and then give an algorithm to approximate both the characteristic power series of the Up operator and eigenvectors of finite slope for Up, and present some explicit examples. We...
متن کاملP-adic Family of Half-integral Weight Modular Forms and Overconvergent Shintani Lifting
Abstract. The goal of this paper is to construct the p-adic analytic family of overconvergent half-integral weight modular forms using Hecke-equivariant overconvergent Shintani lifting. The classical Shintani map(see [Shn]) is the Hecke-equivariant map from the space of cusp forms of integral weight to the space of cusp forms of half-integral weight. Glenn Stevens proved in [St1] that there is ...
متن کاملTHE HALF-INTEGRAL WEIGHT EIGENCURVE by
— In this paper we define Banach spaces of overconvergent half-integral weight p-adic modular forms and Banach modules of families of overconvergent halfintegral weight p-adic modular forms over admissible open subsets of weight space. Both spaces are equipped with a continuous Hecke action for which Up2 is moreover compact. The modules of families of forms are used to construct an eigencurve p...
متن کامل