The Sato-Tate Theorem states that for a non-CM elliptic curve over the rational numbers, the normalized error terms in its point counts over the finite fields modulo each prime are equidistributed according to a specific semicircle-shaped distribution as the prime varies. Conjectured independently by Mikio Sato and John Tate, it was proved in the mid-2000s for a broad class of elliptic curves by Michael Harris, Richard Taylor and collaborators, building on the same modularity-lifting techniques developed for the proof of Fermats Last Theorem.
Facts
Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Sato-Tate conjecture (Wikipedia)
Proof sectionQuote, Proof section
In 2011, Barnet-Lamb, Geraghty, Harris, and Taylor proved a generalized version of the Sato-Tate conjecture
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