4 citations · 8 across the 6 of their papers we have counts for
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On Pair Correlation of Sequences
Gerhard Larcher, Wolfgang Stockinger
We give a survey on the concept of Poissonian pair correlation (PPC) of sequences in the unit interval, on existing and recent results and we state a list of open problems. Moreove…
On a multi-dimensional Poissonian pair correlation concept and uniform distribution
Aicke Hinrichs, Lisa Kaltenböck, Gerhard Larcher +2
The aim of the present article is to introduce a concept which allows to generalise the notion of Poissonian pair correlation, a second-order equidistribution property, to higher d…
Some negative results related to Poissonian pair correlation problems
Gerhard Larcher, Wolfgang Stockinger
We say that a sequence in has Poissonian pair correlations if \begin{equation*} \lim_{N \to \infty} \frac{1}{N} \# \left \lbrace 1 \leq l \neq m…
Pair correlation of sequences with maximal order of additive energy
Gerhard Larcher, Wolfgang Stockinger
We show for sequences of distinct positive integers with maximal order of additive energy, that the sequence $\left(\left\{a_{n} α\right\}\r…
The Champernowne constant is not Poissonian
Ísabel Pirsic, Wolfgang Stockinger
We say that a sequence in has Poissonian pair correlations if \begin{equation*} \lim_{N \to \infty} \frac{1}{N} \# \lbrace 1 \leq l \neq m \leq N…
A survey on M. B. Levin's proofs for the exact lower discrepancy bounds of special sequences and point sets
Lisa Kaltenböck, Wolfgang Stockinger
The goal of this overview article is to give a tangible presentation of recent breakthrough works in discrepancy theory by M. B. Levin. These works provide proofs for the exact low…