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Higher order Fourier analysis of multiplicative functions and applications

- N. Frantzikinakis, B. Host
- Mathematics
- 4 March 2014

We prove a structure theorem for multiplicative functions which states that an arbitrary bounded multiplicative function can be decomposed into two terms, one that is approximately periodic and… Expand

Multiple ergodic averages for three polynomials and applications

- N. Frantzikinakis
- Mathematics
- 22 June 2006

We find the smallest characteristic factor and a limit formula for the multi- ple ergodic averages associated to any family of three polynomials and polynomial fam- ilies of the form… Expand

Ergodic averages of commuting transformations with distinct degree polynomial iterates

- Q. Chu, N. Frantzikinakis, B. Host
- Mathematics
- 14 December 2009

We prove mean convergence, as $N\to\infty$, for the multiple ergodic averages $\frac{1}{N}\sum_{n=1}^N f_1(T_1^{p_1(n)}x)\cdot\ldots\cdot f_\ell(T_\ell^{p_\ell(n)}x)$, where $p_1,\ldots,p_\ell$ are… Expand

Multiple recurrence and convergence for sequences related to the prime numbers

- N. Frantzikinakis, B. Host, Bryna Kra
- Mathematics
- 25 July 2006

For any measure preserving system (X, , μ,T) and A ∈ with μ(A) > 0, we show that there exist infinitely many primes p such that (the same holds with p − 1 replaced by p + 1). Furthermore, we show the… Expand

Pointwise convergence for cubic and polynomial ergodic averages of non-commuting transformations

- Q. Chu, N. Frantzikinakis
- Mathematics
- 27 June 2010

We study the limiting behavior of multiple ergodic averages involving several not necessarily commuting measure preserving transformations. We work on two types of averages, one that uses iterates… Expand

The polynomial multidimensional Szemerédi Theorem along shifted primes

- N. Frantzikinakis, B. Host, Bryna Kra
- Mathematics
- 8 September 2010

AbstractIf
$\vec q_1 ,...,\vec q_m $
: ℤ → ℤℓ are polynomials with zero constant terms and E ⊂ ℤℓ has positive upper Banach density, then we show that the set E ∩ (E −
$\vec q_1 $
(p − 1)) ∩ … ∩ (E… Expand

Equidistribution of sparse sequences on nilmanifolds

- N. Frantzikinakis
- Mathematics
- 27 October 2008

AbstractWe study equidistribution properties of nil-orbits (bnx)n∈ℕ when the parameter n is restricted to the range of some sparse sequence that is not necessarily polynomial. For example, we show… Expand

A Hardy field extension of Szemerédi's theorem

- N. Frantzikinakis, M. Wierdl
- Mathematics
- 20 February 2008

Abstract In 1975 Szemeredi proved that a set of integers of positive upper density contains arbitrarily long arithmetic progressions. Bergelson and Leibman showed in 1996 that the common difference… Expand

Multiple recurrence and convergence for hardy sequences of polynomial growth

- N. Frantzikinakis
- Mathematics
- 28 February 2009

We study the limiting behavior of multiple ergodic averages involving sequences of integers that satisfy some regularity conditions and have polynomial growth. We show that for “typical” choices of… Expand

Multiple correlation sequences and nilsequences

- N. Frantzikinakis
- Mathematics
- 2 July 2014

We study the structure of multiple correlation sequences defined by measure preserving actions of commuting transformations. When the iterates of the transformations are integer polynomials we prove… Expand

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