Finding meaning in error terms

By Barry Mazur. 2008

66 citations recorded by the source corpus.

Four decades ago, Mikio Sato and John Tate predicted the shape of probability distributions to which certain “error terms” in number theory conform. Their prediction—known as the Sato-Tate Conjecture—has been verified for an important class of cases, thanks to the recent work of Laurent Clozel, Michael Harris, and Richard Taylor [3], and of Michael Harris, Nicholas Shepherd-Barron, and Richard Taylor [16], combined with Richard Taylor’s most recent [50] which establishes this advance in our understanding.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/57a72be899d750aa072476de03135a53506e967d

How researchers see this paper

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In Algebra and Number Theory

1. Y. Lau
2. Kannan Soundararajan
3. Jie Wu
4. Emmanuel Kowalski
5. Paul D. Nelson
6. Adam J Harper
7. M. Young
8. Kaisa Matomäki

In Mathematical Physics

1. Y. Lau
2. Kannan Soundararajan
3. Jie Wu
4. Emmanuel Kowalski
5. Paul D. Nelson
6. Kaisa Matomäki
7. M. Young
8. P. Michel

Citations in the corpus

• On modular signs (2009, background): “The main remark is that, underlying most of the problems we consider is the Sato-Tate conjecture, which we recall (see Mazur’s survey [14]): provided f is not of CM type (for instance, if N is squarefree), one should have lim x→+∞ 1 π(x) |{p 6 x | θf(p) ∈ [α, β]}| = ∫ β α dμST”