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, which is always an integer.

For Sato-Tate groups of odd weight we have $t=-a_1$ and the moment sequences of $t$ and $a_1$ coincide because their distributions are symmetric about zero.

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- Review status: reviewed
- Last edited by Andrew Sutherland on 2021-01-01 15:33:18

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

- 2021-01-01 15:33:18 by Andrew Sutherland (Reviewed)
- 2021-01-01 15:33:02 by Andrew Sutherland
- 2021-01-01 15:28:51 by Andrew Sutherland
- 2019-04-20 14:05:03 by Kiran S. Kedlaya (Reviewed)
- 2018-06-20 04:14:34 by Kiran S. Kedlaya

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