Triple product \(p\)-adic \(L\)-functions associated to finite slope \(p\)-adic families of modular forms
It is known for a while how to attach a \(p\)-adic \(L\)-function to a triple of Hida families (or ordinary \(p\)-adic families). However the definition of such \(p\)-adic \(L\)-function does not make sense in the case of finite slope \(p\)-adic families. This paper introduces a new method to handle the case of finite slope families. One views the finite slope families of modular forms as overconvergent sections of the modular sheaves. The construction is a geometric one. Indeed this is an application of a very general geometric construction that the authors developed, called the vector bundles with marked sections. In an earlier paper [Contrib. Math. Comput. Sci. 7, 401--441 (2014; Zbl 1328.11052)], \textit{E. Urban} had claimed a construction for the finite slope families. However this is a gap in that paper. In an appendix of this paper, Urban fixed the gap using results of this paper.
scientific article; zbMATH DE number 7369865
scientific article