G. Larcher

activity

20132025

most citedMetric results on the discrepancy of sequences

(a_{n} α)_{n \geq 1}

modulo one for integer sequences

(a_{n})_{n \geq 1}

of polynomial growth

6 citations · 28 across the 18 of their papers we have counts for

collaborators

Showing 2016 · math.NTShow all

4 papers · 2 filters

math.NT2016★ 3 cited

On pair correlation and discrepancy

Sigrid Grepstad, Gerhard Larcher

We say that a sequence ${x_{n}}_{n \geq 1}$ in $[0, 1)$ has Poissonian pair correlations if \begin{equation*} \lim_{N \rightarrow \infty} \frac{1}{N} \# \left\{ 1 \leq l \neq m \leq…

math.NT2016

On Weyl products and uniform distribution modulo one

Christoph Aistleitner, Gerhard Larcher, Friedrich Pillichshammer +2

In the present paper we study the asymptotic behavior of trigonometric products of the form $\prod_{k = 1}^{N} 2 sin (π x_{k})$ for $N \to \infty$ , where the numbers $ω = (x_{k})_{k = 1}^{N}$ are…

math.NT2016

Additive Energy and Irregularities of Distribution

Christoph Aistleitner, Gerhard Larcher

We consider strictly increasing sequences $(a_{n})_{n \geq 1}$ of integers and sequences of fractional parts $({a_{n} α})_{n \geq 1}$ where $α\in…

math.NT2016

Additive Energy and the Hausdorff dimension of the exceptional set in metric pair correlation problems

Christoph Aistleitner, Gerhard Larcher, Mark Lewko

For a sequence of integers ${a (x)}_{x \geq 1}$ we show that the distribution of the pair correlations of the fractional parts of ${⟨ α a (x)⟩}_{x \geq 1}$ is asymp…