Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Gaetan Chenevier
Affiliation:

Université Paris-Sud
Date:

Mon, 2018-03-12 15:00 - 16:00 Let $E$ be a number field, $N$ an ideal of its ring of integers, and $w \geq 0$ an integer. Consider the set of cuspidal algebraic automorphic representations of $GL_n$ over $E$ whose conductor is $N$, and whose ''weights'' are in the interval $\{0,\dots,w\}$ (with $n$ varying). If the root-discriminant of $E$ is less than a certain explicit function $f$ of $w$, then I show that this set is finite. For instance, we have $f(w)>1$ if, and only if, $w<24$. Under a suitable form of GRH, we may replace $f(w)$ by $8*\Pi*e^{-\psi(1+w)}$, where $\psi$ is the classical digamma function.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/7438