1,098 research outputs found

    Bounded gaps between primes in special sequences

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    We use Maynard's methods to show that there are bounded gaps between primes in the sequence {⌊nΞ±βŒ‹}\{\lfloor n\alpha\rfloor\}, where Ξ±\alpha is an irrational number of finite type. In addition, given a superlinear function ff satisfying some properties described by Leitmann, we show that for all mm there are infinitely many bounded intervals containing mm primes and at least one integer of the form ⌊f(q)βŒ‹\lfloor f(q)\rfloor with qq a positive integer.Comment: 14 page

    Three topics in additive prime number theory

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    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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