# Multidimensional Heilbronn sets

Abstract : We show in the context of $\mathbb{Z}^k$-actions that every van der Corput set is a Heilbronn set. Furthermore we establish Diophantine inequalities of the Heilbronn type for generalized polynomials $g$ in particular for sequences $\nu(n)=\lfloor n^c\rfloor+n^k$ with $c>1$ a non-integral real number and $k\in\mathbb{N}$, as well as for $\nu(p)$ where $p$ runs through all prime numbers.
Document type :
Preprints, Working Papers, ...

https://hal.archives-ouvertes.fr/hal-01333682
Submitted on : Saturday, June 18, 2016 - 5:09:20 PM
Last modification on : Wednesday, October 10, 2018 - 1:37:59 PM

### Identifiers

• HAL Id : hal-01333682, version 1
• ARXIV : 1606.03049

### Citation

Manfred G. Madritsch, Robert F. Tichy. Multidimensional Heilbronn sets. 2016. ⟨hal-01333682⟩

Record views