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p-adic Rankin-Selberg L-functions in universal deformation families

组织者

刁晗生 , 杜衡 , 胡悦科 , Bin Xu , Yihang Zhu

演讲者

Zeping Hao

时间

2025年04月10日 10:00 至 11:00

地点

Shuangqing-C654

摘要

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.