Zobrazeno 1 - 10
of 26
pro vyhledávání: '"Richter, Florian Karl"'
Publikováno v:
Int. Math. Res. Not. IMRN (2), 11488-11512, 2024
We consider vanishing properties of exponential sums of the Liouville function $\lambda$ of the form $$ \lim_{H\to\infty}\limsup_{X\to\infty}\frac{1}{\log X}\sum_{m\leq X}\frac{1}{m}\sup_{\alpha\in C}\bigg|\frac{1}{H}\sum_{h\leq H}\lambda(m+h)e^{2\pi
Externí odkaz:
http://arxiv.org/abs/2310.05528
Publikováno v:
Ann. of Math. (2) 189 (2019), no. 2, 605-652
In this paper we show that every set $A \subset \mathbb{N}$ with positive density contains $B+C$ for some pair $B,C$ of infinite subsets of $\mathbb{N}$, settling a conjecture of Erd\H{o}s. The proof features two different decompositions of an arbitr
Externí odkaz:
http://arxiv.org/abs/1803.00498
Publikováno v:
Number Theory - Diophantine Problems, Uniform Distribution and Applications, Festschrift in Honour of Robert F. Tichy's 60th Birthday, Springer 2017, ISBN 978-3-319-55356-6
Let $k\in\mathbb{N}$ and let $f_1,\ldots,f_k$ belong to a Hardy field. We prove that under some natural conditions on the $k$-tuple $(f_1,\ldots,f_k)$ the density of the set $$ \big\{n\in \mathbb{N}: \text{gcd}(n,\lfloor f_1(n)\rfloor,\ldots,\lfloor
Externí odkaz:
http://arxiv.org/abs/1611.08044
Publikováno v:
Adv. Math. 321 (Dec 2017), pp. 269--286
Answering a question posed by Bergelson and Leibman in [6], we establish a nilpotent version of the polynomial Hales-Jewett theorem that contains the main theorem in [6] as a special case. Important to the formulation and the proof of our main theore
Externí odkaz:
http://arxiv.org/abs/1607.05320
Autor:
Moreira, Joel, Richter, Florian Karl
Publikováno v:
European Journal of Combinatorics, Volume 54, May 2016, Pages 163--176
In 1977 L.T. Ramsey showed that any sequence in $\mathbb{Z}^2$ with bounded gaps contains arbitrarily many collinear points. Thereafter, in 1980, C. Pomerance provided a density version of this result, relaxing the condition on the sequence from havi
Externí odkaz:
http://arxiv.org/abs/1501.07550
Publikováno v:
In Advances in Mathematics 1 December 2017 321:269-286
Publikováno v:
Bulletin of the American Mathematical Society. 59:569-606
Katznelson’s Question is a long-standing open question concerning recurrence in topological dynamics with strong historical and mathematical ties to open problems in combinatorics and harmonic analysis. In this article, we give a positive answer to
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1431165fd74da51a30b8c2b1b5272592
https://doi.org/10.1090/bull/1764
https://doi.org/10.1090/bull/1764
Autor:
Moreira, Joel, Richter, Florian Karl
Publikováno v:
In European Journal of Combinatorics May 2016 54:163-176
Publikováno v:
Discrete Analysis (2021)
We study multicorrelation sequences arising from systems with commuting transformations. Our main result is a refinement of a decomposition result of Frantzikinakis and it states that any multicorrelation sequences for commuting transformations can b
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2762f82e907244f3836a8e1e6698300a
http://arxiv.org/abs/2001.11523
http://arxiv.org/abs/2001.11523
In this work we study the set of eventually always hitting points in shrinking target systems. These are points whose long orbit segments eventually hit the corresponding shrinking targets for all future times. We focus our attention on systems where
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7d4c22909a510ab566978bb9e4d57586
http://arxiv.org/abs/1904.08584
http://arxiv.org/abs/1904.08584