Zobrazeno 1 - 10
of 258
pro vyhledávání: '"Aistleitner, Christoph"'
We disprove a folklore conjecture stating that a sequence in $[0,1]$ with exponential gap distribution must necessarily be uniformly distributed.
Comment: The second version contains minor corrections
Comment: The second version contains minor corrections
Externí odkaz:
http://arxiv.org/abs/2312.08289
It is a classical observation that lacunary function systems exhibit many properties which are typical for systems of independent random variables. However, it had already been observed by Erd\H{o}s and Fortet in the 1950s that probability theory's l
Externí odkaz:
http://arxiv.org/abs/2310.20257
In this paper we present the theory of lacunary trigonometric sums and lacunary sums of dilated functions, from the origins of the subject up to recent developments. We describe the connections with mathematical topics such as equidistribution and di
Externí odkaz:
http://arxiv.org/abs/2301.05561
In this paper, we study distributional properties of the sequence of partial quotients in the continued fraction expansion of fractions $a/N$, where $N$ is fixed and $a$ runs through the set of mod $N$ residue classes which are coprime with $N$. Our
Externí odkaz:
http://arxiv.org/abs/2210.14095
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:
http://arxiv.org/abs/2202.00936
Autor:
Aistleitner, Christoph, Borda, Bence
In his influential paper on quantum modular forms, Zagier developed a conjectural framework describing the behavior of certain quantum knot invariants under the action of the modular group on their arguments. More precisely, when $J_{K,0}$ denotes th
Externí odkaz:
http://arxiv.org/abs/2110.07407
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 $\{a_n \alpha \bmod 1, 1 \leq n \leq N\}$ as $N \to \infty$, valid for Lebesgue-almost all $\alp
Externí odkaz:
http://arxiv.org/abs/2108.02227
Autor:
Aistleitner, Christoph, Borda, Bence
Publikováno v:
Alg. Number Th. 17 (2023) 667-717
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:
http://arxiv.org/abs/2104.01379
Let $(a_k)_{k\in\mathbb N}$ be a sequence of integers satisfying the Hadamard gap condition $a_{k+1}/a_k>q>1$ for all $k\in\mathbb N$, and let $$ S_n(\omega) = \sum_{k=1}^n\cos(2\pi a_k \omega),\qquad n\in\mathbb N,\;\omega\in [0,1]. $$ The lacunary
Externí odkaz:
http://arxiv.org/abs/2012.05281
Koksma's equidistribution theorem from 1935 states that for Lebesgue almost every $\alpha>1$, the fractional parts of the geometric progression $(\alpha^{n})_{n\geq1}$ are equidistributed modulo one. In the present paper we sharpen this result by sho
Externí odkaz:
http://arxiv.org/abs/2010.10355