Zobrazeno 1 - 8
of 8
pro vyhledávání: '"Agamemnon Zafeiropoulos"'
Autor:
Agamemnon Zafeiropoulos, Sam Chow
Publikováno v:
Mathematika. 67:639-646
We establish a strong form of Littlewood's conjecture with inhomogeneous shifts, for a full-dimensional set of pairs of badly approximable numbers on a vertical line. We also prove a uniform assertion of this nature, generalising a strong form of a r
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9e9e361781c8b2234e3202de1d2e1492
https://doi.org/10.1112/mtk.12095
https://doi.org/10.1112/mtk.12095
Autor:
Agamemnon Zafeiropoulos, Marc Technau
Publikováno v:
Acta Arithmetica. 197:93-104
Let $f\colon\mathbb{N}\rightarrow\mathbb{C}$ be an arithmetic function and consider the Beatty set $\mathcal{B}(\alpha) = \lbrace\, \lfloor n\alpha \rfloor : n\in\mathbb{N} \,\rbrace$ associated to a real number $\alpha$, where $\lfloor\xi\rfloor$ de
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::45ee92f429776b2ab5bb3c403e213f71
https://doi.org/10.4064/aa200128-10-6
https://doi.org/10.4064/aa200128-10-6
Publikováno v:
The Quarterly Journal of Mathematics. 71:573-597
Let $(n_k)_{k=1}^{\infty }$ be a lacunary sequence of integers. We show that if $\mu$ is a probability measure on $[0,1)$ such that $|\widehat{\mu }(t)|\leq c|t|^{-\eta }$, then for $\mu$-almost all $x$, the discrepancy $D_N(n_kx)$ satisfies $$\begin
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https://doi.org/10.1093/qmathj/haz058
https://doi.org/10.1093/qmathj/haz058
Let $F \subseteq [0,1]$ be a set that supports a probability measure $��$ with the property that $ |\widehat��(t)| \ll (\log |t|)^{-A}$ for some constant $ A > 0 $. Let $\mathcal{A}= (q_n)_{n\in \mathbb{N}} $ be a sequence of natural numbers.
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::05a91b95f0ddade706fee1e1c2b60e42
https://eprints.whiterose.ac.uk/170428/1/InhomM_0sv.pdf
https://eprints.whiterose.ac.uk/170428/1/InhomM_0sv.pdf
Autor:
Manuel Hauke, Agamemnon Zafeiropoulos
We show that any sequence $(x_n)_{n \in \mathbb{N}} \subseteq [0,1]$ that has Poissonian correlations of $k$-th order is uniformly distributed, also providing a quantitative description of this phenomenon. Additionally, we extend connections between
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ebe3943f9bce6aa762edcea9fae0eba1
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,
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The Duffin-Schaeffer conjecture is a fundamental unsolved problem in metric number theory. It asserts that for every non-negative function $\psi:~\mathbb{N} \rightarrow \mathbb{R}$ for almost all reals $x$ there are infinitely many coprime solutions
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http://arxiv.org/abs/1803.05703
http://arxiv.org/abs/1803.05703
We establish a refinement of Marstrand's projection theorem for Hausdorff dimension functions finer than the usual power functions, including an analogue of Marstrand's Theorem for logarithmic Hausdorff dimension.
Comment: With an Appendix: The
Comment: With an Appendix: The
Externí odkaz:
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