# Polynomial configurations in the primes

• Julia Wolf (Paris)
• Wednesday 30 January 2013, 16:00-17:00
• MR11, CMS.

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.

This talk is part of the Discrete Analysis Seminar series.