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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.

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