Zobrazeno 1 - 10
of 673
pro vyhledávání: '"11K38"'
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
Autor:
Dick, Josef, Pillichshammer, Friedrich
In this short note we report on a coincidence of two mathematical quantities that, at first glance, have little to do with each other. On the one hand, there are the Lebesgue constants of the Walsh function system that play an important role in appro
Externí odkaz:
http://arxiv.org/abs/2412.03164
We investigate the distribution of modular inverses modulo positive integers $c$ in a large interval. We provide upper and lower bounds for their box, ball and isotropic discrepancy, thereby exhibiting some deviations from random point sets. The anal
Externí odkaz:
http://arxiv.org/abs/2411.17823
Autor:
Carneiro, Emanuel, Das, Mithun Kumar
In this paper we provide a detailed study on effective versions of the celebrated Bilu's equidistribution theorem for Galois orbits of sequences of points of small height in the $N$-dimensional algebraic torus, identifying the qualitative dependence
Externí odkaz:
http://arxiv.org/abs/2411.16294
The mean squared error and regularized versions of it are standard loss functions in supervised machine learning. However, calculating these losses for large data sets can be computationally demanding. Modifying an approach of J. Dick and M. Feischl
Externí odkaz:
http://arxiv.org/abs/2409.13453
We study the integration problem over the $s$-dimensional unit cube on four types of Banach spaces of integrands. First we consider Haar wavelet spaces, consisting of functions whose Haar wavelet coefficients exhibit a certain decay behavior measured
Externí odkaz:
http://arxiv.org/abs/2409.12879
Autor:
Robertson, Steven
The discrepancy of a sequence measures how quickly it approaches a uniform distribution. Given a natural number $d$, any collection of one-dimensional so-called low discrepancy sequences $\left\{S_i:1\le i \le d\right\}$ can be concatenated to create
Externí odkaz:
http://arxiv.org/abs/2409.05469
Autor:
Grepstad, Sigrid
We show that given a lattice $\Gamma \subset \mathbb{R}^m \times \mathbb{R}^n$, and projections $p_1$ and $p_2$ onto $\mathbb{R}^m$ and $\mathbb{R}^n$ respectively, cut-and-project sets obtained using Jordan measurable windows $W$ and $W'$ in $\mathb
Externí odkaz:
http://arxiv.org/abs/2409.05450
Autor:
Beretti, Thomas
This work investigates the relation between the Fourier transform of a planar convex body and its geometric properties. The second matter of study is the quadratic discrepancy of planar convex bodies, and we present sharp results on its asymptotic be
Externí odkaz:
http://arxiv.org/abs/2408.15412
Autor:
Das, Mithun Kumar
We estimate the number of zeros of a polynomial in $\mathbb{C}[z]$ within any small circular disc centered on the unit circle, which improves and comprehensively extends a result established by Borwein, Erd{\'e}lyi, and Littmann~\cite{BE1} in 2008. F
Externí odkaz:
http://arxiv.org/abs/2407.15306