1,098 research outputs found
Bounded gaps between primes in special sequences
We use Maynard's methods to show that there are bounded gaps between primes
in the sequence , where is an irrational
number of finite type. In addition, given a superlinear function satisfying
some properties described by Leitmann, we show that for all there are
infinitely many bounded intervals containing primes and at least one
integer of the form with a positive integer.Comment: 14 page
Three topics in additive prime number theory
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.Comment: 40 pages, notes to accompany my lectures at the Current Developments
in Mathematics Conference, Harvard, 16th-17th November 200
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