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Polymath8: Writing the paper 17 Aug 2013 | 02:12 pm
The main objectives of the polymath8 project, initiated back in June, were to understand the recent breakthrough paper of Zhang establishing an infinite number of prime gaps bounded by a fixed constan...
An improved Type I estimate 28 Jul 2013 | 07:54 am
As in all previous posts in this series, we adopt the following asymptotic notation: is a parameter going off to infinity, and all quantities may depend on unless explicitly declared to be “fixed”. Th...
Computing convolutions of measures 27 Jul 2013 | 04:49 am
If and are two absolutely integrable functions on a Euclidean space , then the convolution of the two functions is defined by the formula A simple application of the Fubini-Tonelli theorem shows that...
The Riemann hypothesis in various settings 20 Jul 2013 | 03:31 am
[Note: the content of this post is standard number theoretic material that can be found in many textbooks (I am relying principally here on Iwaniec and Kowalski); I am not claiming any new progress on...
A cheap version of the Kabatjanskii-Levenstein bound for almost orthogonal vectors 18 Jul 2013 | 09:39 pm
Let be a natural number. We consider the question of how many “almost orthogonal” unit vectors one can place in the Euclidean space . Of course, if we insist on being exactly orthogonal, so that for a...
Local universality of zeroes of random polynomials 18 Jul 2013 | 07:21 am
Van Vu and I have just uploaded to the arXiv our joint paper “Local universality of zeroes of random polynomials“. This paper is a sequel to our previous work on local universality of eigenvalues of (...
A physical space proof of the bilinear Strichartz and local smoothing estimates for the Schrodinger equation 10 Jul 2013 | 09:13 pm
The purpose of this post is to link to a short unpublished note of mine that I wrote back in 2010 but forgot to put on my web page at the time. Entitled “A physical space proof of the bilinear Stricha...
The distribution of primes in doubly densely divisible moduli 8 Jul 2013 | 12:15 pm
As in previous posts, we use the following asymptotic notation: is a parameter going off to infinity, and all quantities may depend on unless explicitly declared to be “fixed”. The asymptotic notation...
Bounded gaps between primes (Polymath8) – a progress report 1 Jul 2013 | 01:38 am
For any , let denote the assertion that there are infinitely many pairs of consecutive primes whose difference is at most , or equivalently that thus for instance is the notorious twin prime conjectu...
The distribution of primes in densely divisible moduli 24 Jun 2013 | 10:13 am
As in previous posts, we use the following asymptotic notation: is a parameter going off to infinity, and all quantities may depend on unless explicitly declared to be “fixed”. The asymptotic notation...
