Sato-Tate distributions on Abelian surfaces

Taylor, Noah

doi:10.1090/tran/8025

Sato-Tate distributions on Abelian surfaces
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Trans. Amer. Math. Soc. 373 (2020), 3541-3559 Request permission

Abstract:

We prove a few new cases of the Sato-Tate conjecture, using a new automorphy theorem of Allen et al. Then, in the unproven cases, we use partial results to describe nontrivial asymptotics on the trace of Frobenius, and prove their optimality given current knowledge.

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