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The trace zero density of a Sato-Tate group is the probability that a randomly sampled element (chosen according to the Haar measure) has trace zero.

On each component of a Sato-Tate group, the trace is either constant and equal to zero, or varies continuously taking each particular value with probability zero; so this probability is simply the ratio of the number of components on which the trace is identically zero to the total number of components.

Knowl status:
  • Review status: reviewed
  • Last edited by Andrew Sutherland on 2021-01-01 15:33:52
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