show · st_group.trace_moments all knowls · up · search:

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.

Knowl status:
  • Review status: reviewed
  • Last edited by Kiran S. Kedlaya on 2019-04-20 14:05:03
Referred to by:
History: (expand/hide all) Differences (show/hide)