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Heuristic limitations of the circle method

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 : The n-Category Caf (3 years ago)

Workshop on category theoretic methods in representation theory. Read Post

The (hypothetical) phase diagram of a statistical or computational method

Academics / Mathematics : Statistical Modeling, Causal Inference, and Social Science (16 hours ago)

So here’s the deal. You have a new idea, call it method C, and you try it out on problems X, Y, and Z and it works well—it destroys the existing methods A and B. And then you publish a paper with the pithy title, Method C Wins. And,... Read Post

Williams’ P+1 Factorization Algorithm

Academics / Mathematics : Programming Praxis (5 years ago)

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... Read Post

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