Time: 14:00-15:00 September 23, 2024 (Monday)
Venue: MCM410
Title: p-adic Rankin-Selberg L-functions in universal deformation families
Abstract: We construct a $p$-adic Rankin--Selberg $L$-function associated to the product of two families of modular forms, where the first is an ordinary (Hida) family, and the second an arbitrary universal-deformation family (without any ordinarity condition at $p$). This gives a function on a 4-dimensional base space -- strictly larger than the ordinary eigenvariety, which is 3-dimensional in this case. We state an interpolation formula, which shows our $p$-adic $L$-function interpolates all critical values of the Rankin--Selberg $L$-functions for the classical specialisations of our family, and derive a functional equation for our $p$-adic $L$-function.
