## EVENT DETAILS AND ABSTRACT

**Dynamical Systems Seminar**
**Title:** A Hardy Field Extension of Szemeredi's Theorem

**Speaker:** Nikos Frantzikinakis

**Speaker Info:** University of Memphis

**Brief Description:**

**Special Note**:

**Abstract:**

In 1975 Szemeredi proved that every subset of the integers
with positive density contains arbitrarily long arithmetic
progressions. Bergelson and Leibman showed in 1996 that the common
difference of the arithmetic progression can be a square, a cube, or
more generally of the form p(n) where p(n) is any integer polynomial
with zero constant term. We produce a variety of new results of this
type. We show that the common difference can be of the form [n^c]
where c is any positive real number, or more generally of the form
[a(n)] where a(x) is any function that belongs to some Hardy field
and satisfies some mild growth conditions. This allows us for example
to deal with the class of logarithmico-exponential functions, i.e.,
functions that can be constructed by a finite combination of the
ordinary arithmetical symbols, the real constants, and the functions
e^x, log x . This is joint work with Mate Wierdl.

**Date:** Tuesday, May 06, 2008

**Time:** 3:00pm

**Where:** Lunt 105

**Contact Person:** Prof. Bryna Kra

**Contact email:** kra@math.northwestern.edu

**Contact Phone:** 847-491-5567

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Department of Mathematics, Northwestern University.