Zobrazeno 1 - 10
of 73
pro vyhledávání: '"Christoph Aistleitner"'
Autor:
Christoph Aistleitner, Bence Borda
Publikováno v:
Mathematische Zeitschrift. 302:759-782
In this paper we study the relation between the function $J_{4_1,0}$, which arises from a quantum invariant of the figure-eight knot, and Sudler's trigonometric product. We find $J_{4_1,0}$ up to a constant factor along continued fraction convergents
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cc06800bc4a120c5b54ad5ad2712c609
https://doi.org/10.1007/s00209-022-03086-5
https://doi.org/10.1007/s00209-022-03086-5
Autor:
Christoph Aistleitner, Simon Baker
Publikováno v:
Israel Journal of Mathematics. 242:243-268
A classical theorem of Koksma states that for Lebesgue almost every $x>1$ the sequence $(x^n)_{n=1}^{\infty}$ is uniformly distributed modulo one. In the present paper we extend Koksma's theorem to the pair correlation setting. More precisely, we sho
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::04b90ef2b924c696b236dd8142d873c2
https://doi.org/10.1007/s11856-021-2130-4
https://doi.org/10.1007/s11856-021-2130-4
Let $\psi: \mathbb{N} \to [0,1/2]$ be given. The Duffin-Schaeffer conjecture, recently resolved by Koukoulopoulos and Maynard, asserts that for almost all reals $\alpha$ there are infinitely many coprime solutions $(p,q)$ to the inequality $|\alpha -
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e7490ce8a5adb51048929a8935609571
Publikováno v:
The Quarterly Journal of Mathematics. 70:831-848
In recent years, a variant of the resonance method was developed which allowed to obtain improved Ω-results for the Riemann zeta function along vertical lines in the critical strip. In the present paper, we show how this method can be adapted to pro
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::713b61d732382299d15599d017300c38
https://doi.org/10.1093/qmath/hay067
https://doi.org/10.1093/qmath/hay067
Let $(a_n)_{n \geq 1}$ be a sequence of distinct positive integers. In a recent paper, Rudnick established asymptotic upper bounds for the minimal gaps of $\{a_n \alpha \mod 1, ~1 \leq n \leq N\}$ as $N \to \infty $, valid for Lebesgue-almost all $\a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b3baf1e9ef82639ce8d3f444891654ce
Autor:
Christoph Aistleitner, Bence Borda
There is an extensive literature on the asymptotic order of Sudler's trigonometric product $P_N (\alpha) = \prod_{n=1}^N |2 \sin (\pi n \alpha)|$ for fixed or for "typical" values of $\alpha$. In the present paper we establish a structural result, wh
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::38cc4b5b46986c74c4068ee68a6a18dd
The pair correlation is a localized statistic for sequences in the unit interval. Pseudo-random behavior with respect to this statistic is called Poissonian behavior. The metric theory of pair correlations of sequences of the form $$(a_n \alpha )_{n
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b5a8f89a12f3a9c0352976cd54461987
Publikováno v:
Transactions of the American Mathematical Society. 372:4425-4446
We give metric theorems for the property of Borel normality for real numbers under the assumption of digit dependencies in their expansion in a given integer base. We quantify precisely how much digit dependence can be allowed such that, still, almos
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ddbf2961a987b9a483b47e5e67903ae3
https://doi.org/10.1090/tran/7706
https://doi.org/10.1090/tran/7706
Publikováno v:
Israel Journal of Mathematics. 222:463-485
For a sequence of integers $\{a(x)\}_{x \geq 1}$ we show that the distribution of the pair correlations of the fractional parts of $\{ \langle \alpha a(x) \rangle \}_{x \geq 1}$ is asymptotically Poissonian for almost all $\alpha$ if the additive ene
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8788c783242c66799bc343856e745c14
https://doi.org/10.1007/s11856-017-1597-5
https://doi.org/10.1007/s11856-017-1597-5
Autor:
Gerhard Larcher, Christoph Aistleitner
Publikováno v:
Uniform distribution theory. 12:99-107
We consider strictly increasing sequences $\left(a_{n}\right)_{n \geq 1}$ of integers and sequences of fractional parts $\left(\left\{a_{n} \alpha\right\}\right)_{n \geq 1}$ where $\alpha \in \mathbb{R}$. We show that a small additive energy of $\lef
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6a94e96227ae70795e87e350d3489b21
https://doi.org/10.1515/udt-2017-0006
https://doi.org/10.1515/udt-2017-0006