BIMSA >
BIMSA-YMSC Tsinghua Number Theory Seminar
p-adic Rankin-Selberg L-functions in universal deformation families
p-adic Rankin-Selberg L-functions in universal deformation families
Organizers
Hansheng Diao
, Heng Du
, Yueke Hu
, Bin Xu
, Yihang Zhu
Speaker
Zeping Hao
Time
Thursday, April 10, 2025 10:00 AM - 11:00 AM
Venue
Shuangqing-C654
Abstract
In this talk, I will outline the construction of $p$-adic Rankin-Selberg L-functions associated to the product of two families of modular forms, beyond the known cases of eigenvarieties. It will be formulated in the natural language of Galois deformations. The parameter space, arising from the product of an ordinary deformation space and a universal deformation space, is of dimension 4, and is strictly larger than the three-dimensional eigenvariety in this case. The extra dimension is reflected in the interpolation range, which includes infinite slope modular forms in the second family (and are otherwise absent in the Hida or Coleman case). I will also discuss a new type of functional equation for this $p$-adic L-function using universal gamma factors. This is a joint work with David Loeffler.