# p-adic interpolation of $$GL_n$$-automorphic L-functions

19.05.2020 13:15 - 14:45

Jeanine Van Order (University of Bielefeld)

The construction of p-adic L-functions forms an important first step for Iwasawa-Greenberg main conjectures and variants, leading to insight on the structure of corresponding Selmer groups consistent with the predictions of Birch and Swinnerton-Dyer. I will explain such a starting point for developing higher-rank analogues of the existing theory for $$GL_2$$ in anticyclotomic towers. To be more precise, fix $$n \geq 2$$ an integer, and K a CM field. Let $$\pi$$ be a cuspidal automorphic representation of $$GL_n(\mathbb A_K)$$ which is ordinary at a given prime P of K. Using the theory of Eulerian integral presentations with essential Whittaker vectors, I will explain how to construct from some well-chosen pure tensor a p-adic interpolation series for algebraic parts of the degree n L-function $$L(s, \pi \otimes \chi)$$ at critical points $$s= s_0$$, where $$\chi$$ varies over ring class characters factoring through the anticyclotomic tower. If time permits, then I will also outline one or two potential applications.

Organiser:

#### H. Grobner, A. Minguez-Espallargas, A. Mellit

Location:
Zoom ID: 431 655 310