Photo by brambro from unsplash
We establish Diophantine inequalities for the fractional parts of generalized polynomials $f$, 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… Click to show full abstract
We establish Diophantine inequalities for the fractional parts of generalized polynomials $f$, 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. This is related to classical work of Heilbronn and to recent results of Bergelson \textit{et al.}
Keywords:
van der;
der corput;
corput sets;
multidimensional van;
sets small;
fractional parts
Journal Title: Mathematika
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!
Journal Title: Mathematika
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!