p -adic interpolation of Gauss–Manin connections on nearly overconvergent modular forms and p -adic L -functions

Abstract

Abstract In this paper, we give a new geometric definition of nearly overconvergent modular forms and p -adically interpolate the Gauss–Manin connection on this space. This can be seen as an ‘overconvergent’ version of the unipotent circle action on the space of p -adic modular forms, as constructed by Gouvêa and Howe. This improves on results of Andreatta and Iovita and has applications to the construction of Rankin–Selberg and triple-product p -adic L -functions.