One of the most basic methods in additive number theory is the Hardy-Littlewood circle method. This method is based on expressing a quantity of interest to additive number theory, such as the number of representations of an integer as the sum of three primes, as a Fourier-analytic integral over the unit circle involving exponential [...]

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Academics / Mathematics : Terence Tao's Blog

Let be an element of the unit circle, let, and let. We define the (rank one) Bohr set to be the set where is the distance to the origin in the unit circle (or equivalently, the distance to the nearest integer, after lifting up to )....

Academics / Mathematics : Terence Tao's Blog

We have seen in previous notes that the operation of forming a Dirichlet series or twisted Dirichlet series is an incredibly useful tool for questions in multiplicative number theory. Such series can be viewed as a multiplicative Fo...

Academics / Mathematics : The n-Category Caf

Workshop on category theoretic methods in representation theory.

Academics / Mathematics : The n-Category Caf

Young Researchers Workshop on Higher Algebraic and Geometric Structures: Modern Methods in Representation Theory at the Fields Institute, May 7-9, 2012

Academics / Mathematics : Programming Praxis

Hugh Williams invented the p+1 integer factorization method in 1982 based on John Pollard’s p-1 integer factorization method; the p+1 method finds a factor p when p is smooth with respect to a bound B. We noted in a previous exercis...

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