Mario Neumuller

activity

20162021

most citedOn the asymptotic behaviour of the sine product

\prod_{r = 1}^{n} ∣2 sin (π r α) ∣

1 citations · 1 across the 6 of their papers we have counts for

collaborators

7 papers

math.NT2021

On the order of magnitude of Sudler products II

Sigrid Grepstad, Mario Neumüller, Agamemnon Zafeiropoulos

We study the asymptotic behavior of Sudler products $P_{N} (α) = \prod_{r = 1}^{N} 2∣ sin π r α ∣$ for quadratic irrationals $α \in R$ . In particular, we verify the convergence of ce…

math.NT2021

On the asymptotic behavior of Sudler products along subsequences

Mario Neumüller

Let $α \in (0, 1)$ and irrational. We investigate the asymptotic behaviour of sequences of certain trigonometric products (Sudler products) $(P_{N} (α))_{N \in N}$ with $$P_N(α)…

math.NT2019★ 1 cited

On the asymptotic behaviour of the sine product $\prod_{r = 1}^{n} ∣2 sin (π r α) ∣$

Sigrid Grepstad, Lisa Kaltenböck, Mario Neumüller

In this paper we review recently established results on the asymptotic behaviour of the trigonometric product $P_{n} (α) = \prod_{r = 1}^{n} ∣2 sin π r α ∣$ as $n \to \infty$ . We focus on ir…

math.NT2018

A positive lower bound for $lim inf_{N \to \infty} \prod_{r = 1}^{N} ∣ 2 sin π r φ ∣$

Sigrid Grepstad, Lisa Kaltenböck, Mario Neumüller

Nearly 60 years ago, Erdős and Szekeres raised the question of whether $N \to \infty lim inf r = 1 \prod N ∣ 2 sin π r α ∣ = 0$ for all irrationals $α$ . Despite its simp…

math.NT2018

Asymptotic behaviour of the Sudler product of sines for quadratic irrationals

Sigrid Grepstad, Mario Neumüller

We study the asymptotic behaviour of the sequence of sine products $P_{n} (α) = \prod_{r = 1}^{n} ∣2 sin π r α ∣$ for real quadratic irrationals $α$ . In particular, we study the subsequence…

math.NT2017

A reduced fast construction of polynomial lattice point sets with low weighted star discrepancy

Ralph Kritzinger, Helene Laimer, Mario Neumüller

The weighted star discrepancy is a quantitative measure for the performance of point sets in quasi-Monte Carlo algorithms for numerical integration. We consider polynomial lattice…

math.NT2016

Metrical star discrepancy bounds for lacunary subsequences of digital Kronecker-sequences and polynomial tractability

Mario Neumüller, Friedrich Pillichshammer

The star discrepancy $D_{N}^{*} (P)$ is a quantitative measure for the irregularity of distribution of a finite point set $P$ in the multi-dimensional unit cube whic…