Triple product p-adic L-functions associated to finite slope p-adic families of modular forms, with an appendix by Eric Urban

Fabrizio Andreatta; Adrian Iovita

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arXiv · 1708.02785

Triple product p-adic L-functions associated to finite slope p-adic families of modular forms, with an appendix by Eric Urban

Fabrizio Andreatta·Adrian Iovita

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Abstract

We p-adically interpolate the relative de Rham cohomology of the universal elliptic curve over strict neighbourhoods of the ordinary locus of modular curves, together with the Hodge filtration and Gauss-Manin connection. Sections of these sheaves provide the so called nearly overconvergent modular forms. This extends previous work of Andreatta, Iovita and Pilloni where we p-adically interpolate powers of the Hodge bundle and in that case the sections coincide with Coleman overconvergent modular forms. We also show that, under suitable assumptions, one can p-adically interpolate the Gauss-Manin connection. This is used to define p-adic L-functions attached to a triple of p-adic finite slope families of modular forms, generalizing previous constructions for Hida families.

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Fabrizio Andreatta, Adrian Iovita. 2017-08-09. Triple product p-adic L-functions associated to finite slope p-adic families of modular forms, with an appendix by Eric Urban. https://arxiv.org/abs/1708.02785

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