# On the global Gan-Gross-Prasad conjecture for general spin groups

## TL;DR

This paper proposes a global Gan-Gross-Prasad conjecture for general spin groups relating automorphic form periods to L-values, supported by cases for n=2, 3, and some for n=4.

## Contribution

It formulates a new conjecture connecting automorphic periods and L-values for general spin groups and verifies it in specific low-dimensional cases.

## Key findings

- Conjecture holds for n=2 and 3.
- Partial verification for certain cases when n=4.
- Provides a framework for understanding automorphic periods in relation to L-values.

## Abstract

We formulate a global Gan-Gross-Prasad conjecture for general spin groups. That is, we formulate a conjecture on a relation between periods of certain automorphic forms on $GSpin_{n+1} \times GSpin_n$ along the diagonal subgroup $GSpin_n$ and some $L$-values. To support the conjecture, we show that the conjecture holds for $n=2$ and $3$ and for certain cases for $n=4$.