32 citations · 52 across the 5 of their papers we have counts for
5 papers
IPr* recurrence and nilsystems
V. Bergelson, A. Leibman
We prove that nilsystems possess the IPr*-recurrence property and, moreover, are characterized by this property.
Nilsequences, null-sequences, and multiple correlation sequences
Alexander Leibman
A (d-parameter) basic nilsequence is a sequence of the form ψ(n)=f(a^{n}x), n \in Z^{d}, where x is a point of a compact nilmanifold X, a is a translation on X, and f is a continuo…
The shifted primes and the multidimensional Szemeredi and polynomial van der Waerden theorems
Vitaly Bergelson, Alexander Leibman, Tamar Ziegler
In this short note we establish new refinements of multidimensional Szemeredi and polynomial van der Waerden theorems along the shifted primes.
Intersective polynomials and polynomial Szemeredi theorem
Vitaly Bergelson, Alexander Leibman, Emmanuel Lesigne
Let $P=\{p_{1},\ld,p_{r}\}\subset\Q[n_{1},\ld,n_{m}]$ be a family of polynomials such that $p_{i}(\Z^{m})\sle\Z$, $i=1,\ld,r$. We say that the family has {\it PSZ property} if…
Set-polynomials and polynomial extension of the Hales-Jewett Theorem
Vitaly Bergelson, Alexander Leibman
An abstract, Hales-Jewett type extension of the polynomial van der Waerden Theorem [J. Amer. Math. Soc. 9 (1996),725-753] is established: Theorem. Let r,d,q \in \N. There exists N…