##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Nolan Wallach

#### UCSD

## The meromorphic continuation of smooth Eisenstein series

##### Abstract:

In his monumental book 'On the Functional Equations satisfied by Eisenstein Series' Langlands proved that the K-finite Eisenstein series, initially defined, convergent and holomorphic in appropriate open tube of the parameter space can be meromorphically continued to the entire parameter space. The K-finiteness was critical to his proof of the theorem. In this lecture I will show how to use Langlands' theorem to prove the meromorphic continuation for smooth Eisenstein series. These results are valid in the full context of Langlands' theorem but I will only talk about arithmetic groups for which the definitions are easier. (Indeed, Langlands' definition of the groups that that would be studied was only completed at the end of the induction in his notorious chapter 7).

Host: Cristian Popescu

### April 11, 2019

### 2:00 PM

### AP&M 7321

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