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The trace $t$ of a random element of a Sato-Tate group $G$ can be viewed as a random variable whose distribution is given by the pushforward of the Haar measure on $G$ under the trace map.

The $n$th moment $\mathrm{M}_n[t]:= \mathrm{E}[t^n]$ of $t$ is the expected value of the $n$th power of the trace, and it is necessarily an integer.

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• Review status: reviewed
• Last edited by Kiran S. Kedlaya on 2019-04-20 14:05:03
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