The **fourth trace moment** of a Sato-Tate group $G$ is the expected value of the fourth power of the trace of a random element of $G$ (under the Haar measure).

By a result known as "Larsen's alternative" [MR:2058618 ], if the fourth trace moment is less than or equal to 5 then $G$ is irreducible, and for $G$ of odd weight, the fourth trace moment is 3 when $G=\mathrm{USp}(2g)$ and greater than 3 otherwise.

**Authors:**

**Knowl status:**

- Review status: beta
- Last edited by Andrew Sutherland on 2021-05-01 10:18:47

**Referred to by:**

**History:**(expand/hide all)

- 2021-05-01 10:18:47 by Andrew Sutherland
- 2021-05-01 10:18:13 by Andrew Sutherland
- 2021-03-19 21:30:05 by Andrew Sutherland
- 2021-03-19 21:20:11 by Andrew Sutherland

**Differences**(show/hide)