P-adic L-functions in universal deformation families

Abstract

We construct examples of p-adic L-functions over universal deformation spaces for GL(2). We formulate a conjecture predicting that the natural parameter spaces for p-adic L-functions are not the usual eigenvarieties (parametrising nearly-ordinary families of automorphic representations), but other, larger spaces depending on a choice of a parabolic subgroup, which we call "big parabolic eigenvarieties".

14 pages. Updated based on recent results of Y. Ding and K. Nakamura

References in corpus (1)

• Zeta morphisms for rank two universal deformations

Cited by in corpus (4)

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• Iwasawa theory for quadratic Hilbert modular forms