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Theorem

Sato-Tate Theorem

Number Theory

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 Form
Characterization Theorem 1
Proof Year
2011 1
Connections

Has Statement Form

Characterization, Concepts

In Branch

Number Theory, Branches of Mathematics
Source Sato-Tate conjecture (Wikipedia)

Proved By

Laurent Clozel, Mathematicians
Source Sato-Tate conjecture (Wikipedia)
Michael Harris, Mathematicians
Source Sato-Tate conjecture (Wikipedia)
Nicholas Shepherd-Barron, Mathematicians
Source Sato-Tate conjecture (Wikipedia)
Richard Taylor, Mathematicians
Source Sato-Tate conjecture (Wikipedia)
Sources
1. Sato-Tate conjecture (Wikipedia)
  • Proof section
    In 2011, Barnet-Lamb, Geraghty, Harris, and Taylor proved a generalized version of the Sato-Tate conjecture
  • In Branch: Number Theory, Lead
    In mathematics, the Sato-Tate conjecture is a statistical statement about the family of elliptic curves Ep obtained from an elliptic curve E over the rational numbers by reduction modulo almost all prime numbers p.
  • Proved By: Laurent Clozel, Lead
    The original conjecture and its generalization to all totally real fields was proved by Laurent Clozel, Michael Harris, Nicholas Shepherd-Barron, and Richard Taylor under mild assumptions in 2008, and completed by Thomas Barnet-Lamb, David Geraghty, Harris, and Taylor in 2011.
  • Proved By: Michael Harris, Lead
    The original conjecture and its generalization to all totally real fields was proved by Laurent Clozel, Michael Harris, Nicholas Shepherd-Barron, and Richard Taylor under mild assumptions in 2008, and completed by Thomas Barnet-Lamb, David Geraghty, Harris, and Taylor in 2011.
  • Proved By: Nicholas Shepherd-Barron, Lead
    The original conjecture and its generalization to all totally real fields was proved by Laurent Clozel, Michael Harris, Nicholas Shepherd-Barron, and Richard Taylor under mild assumptions in 2008, and completed by Thomas Barnet-Lamb, David Geraghty, Harris, and Taylor in 2011.
  • Proved By: Richard Taylor, Lead
    The original conjecture and its generalization to all totally real fields was proved by Laurent Clozel, Michael Harris, Nicholas Shepherd-Barron, and Richard Taylor under mild assumptions in 2008, and completed by Thomas Barnet-Lamb, David Geraghty, Harris, and Taylor in 2011.
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