# Factorization of arithmetic automorphic periods

## TL;DR

This paper proves that arithmetic automorphic periods for GL_n over CM fields decompose into factors at infinite places, confirming a long-standing conjecture and aligning with Langlands correspondence predictions.

## Contribution

It establishes the factorization of automorphic periods over CM fields, extending Shimura's conjecture and supporting Langlands program predictions.

## Key findings

- Automorphic periods factorize through infinite places.
- Generalizes Shimura's conjecture from 1983.
- Aligns with Langlands correspondence expectations.

## Abstract

In this paper, we prove that the arithmetic automorphic periods for $GL_{n}$ over a CM field factorize through the infinite places. This generalizes a conjecture of Shimura in 1983, and is predicted by the Langlands correspondence between automorphic representations and motives.