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## Polynomial extensions of van der Waerden’s and Szemerédi’s theorems

- V. Bergelson, A. Leibman
- Mathematics
- 1996

An extension of the classical van der Waerden and Szemeredi the- orems is proved for commuting operators whose exponents are polynomials. As a consequence, for example, one obtains the following… Expand

## Pointwise convergence of ergodic averages for polynomial sequences of translations on a nilmanifold

- A. Leibman
- MathematicsErgodic Theory and Dynamical Systems
- 22 December 2004

We show that the orbit of a point on a compact nilmanifold X under the action of a polynomial sequence of translations on X is well distributed on the union of several sub-nilmanifolds of X. This… Expand

## Convergence of multiple ergodic averages along polynomials of several variables

- A. Leibman
- Mathematics
- 1 December 2005

AbstractLetT be an invertible measure preserving transformation of a probability measure spaceX. Generalizing a recent result of Host and Kra, we prove that the averages
$$T^{p1(u)} f$$
converge… Expand

## Distribution of values of bounded generalized polynomials

- V. Bergelson, A. Leibman
- Mathematics
- 6 June 2007

A generalized polynomial is a real-valued function which is obtained from conventional polynomials by the use of the operations of addition, multiplication, and taking the integer part; a generalized… Expand

## Polynomial mappings of groups

- A. Leibman
- Mathematics
- 1 December 2002

A mapping ϕ of a groupG to a groupF is said to be polynomial if it trivializes after several consecutive applications of operatorsDh,h ∈G, defined byDhϕ(g)=ϕ(g)−1ϕ(gh). We study polynomial mappings… Expand

## Polynomial Sequences in Groups

- A. Leibman
- Mathematics
- 1 March 1998

Abstract Given a groupGwith lower central seriesG = G1 ⊇ G2 ⊇ G3 ⊇ ···, we say that a sequenceg: Z → Gispolynomialif for anykthere isdsuch that the sequence obtained fromgby applying the difference… Expand

## A nilpotent Roth theorem

- V. Bergelson, A. Leibman
- Mathematics
- 1 February 2002

Abstract.Let T and S be invertible measure preserving transformations of a probability measure space (X, ℬ, μ). We prove that if the group generated by T and S is nilpotent, then … Expand

## Set-polynomials and polynomial extension of the Hales-Jewett Theorem

- V. Bergelson, A. Leibman
- Mathematics
- 1 July 1999

An abstract, Hales-Jewett type extension of the polynomial van der Waerden Theorem [BL] is established: Theorem. Let r, d, q ∈ N. There exists N ∈ N such that for any r-coloring of the set of subsets… Expand

## Intersective polynomials and the polynomial Szemerédi theorem

- V. Bergelson, A. Leibman, E. Lesigne
- Mathematics
- 25 October 2007

## Orbit of the diagonal in the power of a nilmanifold

- A. Leibman
- Mathematics
- 20 October 2009

Let X be a nilmanifold, that is, a compact homogeneous space of a nilpotent Lie group G, and let a 2 G. We study the closure of the orbit of the diagonal of X r under the action (a p1(n)

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