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Julia Wolf (Paris)
Wednesday 30 January 2013, 16:00-17:00
Polynomial configurations in the primes
- đ¤ Speaker: Julia Wolf (Paris)
- đ Date & Time: Wednesday 30 January 2013, 16:00 - 17:00
- đ Venue: MR11, CMS
Abstract
The Bergelson-Leibman theorem states that if P_1, ... , P_k are polynomials with integer coefficients, then any subset of the integers of positive upper density contains a polynomial configuration x+P_1(m), \dots, x+P_k(m), where x,m are integers. Various generalizations of this theorem are known. Wooley and Ziegler showed that the variable m can in fact be taken to be a prime minus 1, and Tao and Ziegler showed that the Bergelson-Leibman theorem holds for subsets of the primes of positive relative upper density. In this talk we discuss a hybrid of the latter two results, namely that the step m in the Tao-Ziegler theorem can be restricted to the set of primes minus 1. This is joint work with Thai Hoang Le.
Series This talk is part of the Discrete Analysis Seminar series.
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