Zobrazeno 1 - 7
of 7
pro vyhledávání: '"Mario Neumüller"'
Publikováno v:
Proceedings of the American Mathematical Society. 147:4863-4876
Nearly 60 years ago, Erdős and Szekeres raised the question of whether lim inf N → ∞ ∏ r = 1 N | 2 sin π r α | = 0 \begin{equation*} \liminf _{N\to \infty } \prod _{r=1}^N \left | 2\sin \pi r \alpha \right | =0 \end{equation*} for all ir
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::17967239322f24d9e2e6845a4cdc1330
https://doi.org/10.1090/proc/14611
https://doi.org/10.1090/proc/14611
Autor:
Mario Neumüller
Let $\alpha \in (0,1)$ and irrational. We investigate the asymptotic behaviour of sequences of certain trigonometric products (Sudler products) $(P_N(\alpha))_{N\in\mathbb{N}}$ with $$P_N(\alpha) =\prod_{r=1}^N|2\sin(\pi r \alpha)|.$$ More precisely,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::523ae510b9246103d6288b20ba655766
http://arxiv.org/abs/2103.14307
http://arxiv.org/abs/2103.14307
Publikováno v:
International Journal of Number Theory
We study the asymptotic behavior of Sudler products $P_N(\alpha)= \prod_{r=1}^{N}2|\sin \pi r\alpha|$ for quadratic irrationals $\alpha \in \mathbb{R}$. In particular, we verify the convergence of certain perturbed Sudler products along subsequences,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8fc59d9304ea62036693bea8ad393fd6
Autor:
Mario Neumüller, Sigrid Grepstad
Publikováno v:
Journal of Mathematical Analysis and Applications. 465:928-960
We study the asymptotic behaviour of the sequence of sine products P n ( α ) = ∏ r = 1 n | 2 sin π r α | for real quadratic irrationals α. In particular, we study the subsequence Q n ( α ) = ∏ r = 1 q n | 2 sin π r α | , where q n
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0b42f27f84cb354d0cadeac6dc7a86de
https://doi.org/10.1016/j.jmaa.2018.05.045
https://doi.org/10.1016/j.jmaa.2018.05.045
Publikováno v:
Springer Proceedings in Mathematics & Statistics ISBN: 9783319914350
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 point sets, whose generating vectors can be obtained by a component-by
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::96eeaf7214b8db435335df9e3fd5ef94
https://doi.org/10.1007/978-3-319-91436-7_21
https://doi.org/10.1007/978-3-319-91436-7_21
The star discrepancy D N * ( 𝒫 ) $D_N^* \left( {\cal P} \right)$ is a quantitative measure for the irregularity of distribution of a finite point set 𝒫 in the multi-dimensional unit cube which is intimately related to the integration error of q
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6e692e558255b10e443b40531e0bd5c6
http://arxiv.org/abs/1605.00378
http://arxiv.org/abs/1605.00378