Low discrepancy sequences failing Poissonian pair correlations
Sign Up to like & getrecommendations! Published in 2019 at "Archiv der Mathematik"
DOI: 10.1007/s00013-019-01336-3
Abstract: M. Levin defined a real number x that satisfies that the sequence of the fractional parts of $$(2^n x)_{n\ge 1}$$(2nx)n≥1 are such that the first N terms have discrepancy $$O((\log N)^2/ N)$$O((logN)2/N), which is the… read more here.
Keywords: fractional parts; low discrepancy; pair correlations; poissonian pair ... See more keywords
MULTIDIMENSIONAL VAN DER CORPUT SETS AND SMALL FRACTIONAL PARTS OF POLYNOMIALS
Sign Up to like & getrecommendations! Published in 2019 at "Mathematika"
DOI: 10.1112/s0025579318000529
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… read more here.
Keywords: van der; der corput; corput sets; multidimensional van ... See more keywords
On the Range of Arithmetic Means of the Fractional Parts of Harmonic Numbers
Sign Up to like & getrecommendations! Published in 2024 at "Mathematics"
DOI: 10.3390/math12233731
Abstract: In this paper, the limit points of the sequence of arithmetic means 1n∑m=1n{Hm}σ for n=1,2,3,… are studied, where Hm is the mth harmonic number with fractional part {Hm} and σ is a fixed positive constant.… read more here.
Keywords: limit; fractional parts; arithmetic means; means fractional ... See more keywords