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of 348
pro vyhledávání: '"11K06"'
We provide an asymptotic formula for the average value of the sequence A351830: $a_{n} = |P_{n} - y^{2}_{n}|$ for $1 \leq n \leq x$, where $P_{n}$ is the $n$-th square pyramidal number and $y^{2}_{n}$ is the closest square to $P_{n}$. Moreover, we su
Externí odkaz:
http://arxiv.org/abs/2412.10097
It is well known that almost every dilation of a sequence of real numbers, that diverges to $\infty$, is dense modulo~1. This paper studies the exceptional set of points -- those for which the dilation is not dense. Specifically, we consider the Haus
Externí odkaz:
http://arxiv.org/abs/2409.00775
Autor:
Karagulyan, Grigori, Petrosyan, Iren
We give an extension of a criterion of van der Corput on uniform distribution of sequences. Namely, we prove that a sequence $x_n$ is uniformly distributed modulo 1 if it is weakly monotonic and satisfies the conditions $\Delta^2x_n\to 0,\quad n^2\De
Externí odkaz:
http://arxiv.org/abs/2408.07061
Let $(p_n)$ denote the sequence of prime numbers, with $2=p_1
Externí odkaz:
http://arxiv.org/abs/2406.19491
The most versatile version of the classical divergence Borel-Cantelli lemma shows that for any divergent sequence of events $E_n$ in a probability space satisfying a quasi-independence condition, its corresponding limsup set $E_\infty$ has positive p
Externí odkaz:
http://arxiv.org/abs/2406.19198
Autor:
Marklof, Jens
We construct a point set in the Euclidean plane that elucidates the relationship between the fine-scale statistics of the fractional parts of $\sqrt n$ and directional statistics for a shifted lattice. We show that the randomly rotated, and then stre
Externí odkaz:
http://arxiv.org/abs/2406.09107
Autor:
Golafshan, Mehdi, Mitrofanov, Ivan
We investigate unipotent dynamics on a torus and apply these techniques to the following problem. Let \(d\) be a positive integer, and let \(a > 0\) be a real number. For an integer \(b \geqslant 5\), such that \(a\) and \(b\) are multiplicatively in
Externí odkaz:
http://arxiv.org/abs/2402.16210
We provide a construction of binary pseudorandom sequences based on Hardy fields $\mathcal{H}$ as considered by Boshernitzan. In particular we give upper bounds for the well distribution measure and the correlation measure defined by Mauduit and S\'a
Externí odkaz:
http://arxiv.org/abs/2312.08333
In this article, we examine the Poissonian pair correlation (PPC) statistic for higher-dimensional real sequences. Specifically, we demonstrate that for $d\geq 3$, almost all $(\alpha_1,\ldots,\alpha_d) \in \mathbb{R}^d$, the sequence $\big(\{x_n\alp
Externí odkaz:
http://arxiv.org/abs/2310.09541
Let $F $ be a totally real number field and $r=[F :\mathbb{Q}].$ Let $A_k(\mathfrak{N},\omega) $ be the space of holomorphic Hilbert cusp forms with respect to $K_1(\mathfrak{N})$, weight $k=(k_1,\,...\,,k_r)$ with $k_j>2,$ for all $j$ and central He
Externí odkaz:
http://arxiv.org/abs/2307.16736