2007/10/03 by Ben Green, Green, Ben
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.0710.0823
40 pages, notes to accompany my lectures at the Current Developments in Mathematics Conference, Harvard, 16th-17th November 2007
arxiv created 2007/10/03 · arxiv updated 2009/12/01
This is an expository article to accompany my two lectures at the CDM conference. I have used this an excuse to make public two sets of notes I had lying around, and also to put together a short reader's guide to some recent joint work with T.Tao. Contents: 1. An exposition, without much detail, of the work of Goldston, Pintz and Yildirim on gaps between primes; 2. A detailed discussion of the work of Mauduit and Rivat establishing that 50 percent of the primes have odd digit sum when written in base 2; 3. A reader's guide to recent work of T.Tao and the author on linear equations in primes. The sections can be read independently.