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The first $a_2$ moment of a Sato-Tate group $G$ is the expected value of the quadratic coefficient of the characteristic polynomial of a random element of $G$ (under its Haar measure).

When $G$ is the Sato-Tate group of an abelian variety, the first $a_2$ moment is equal to the rank of its Néron–Severi group [arXiv:1910.00518, MR:4038255].

Knowl status:
  • Review status: beta
  • Last edited by Andrew Sutherland on 2021-05-01 10:17:01
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