Related papers: On the error term of a lattice counting problem

We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type structure, where the target vectors are boundably short. For…

Using a recent method developed by Mahatab, we obtain an improved $\Omega$-bound for the error term arising in lattice counting problem of bodies of revolution in $\mathbb R^3$ around a coordinate axis and having smooth boundary with…

We establish a relationship between error terms appearing in estimates for the counting functions of smooth and rough numbers. We then apply this link to obtain an explicit upper bound for the error term in de Bruijn's approximation…

Due to their importance in both data analysis and numerical algorithms, low rank approximations have recently been widely studied. They enable the handling of very large matrices. Tight error bounds for the computationally efficient…

We study the error of the number of unimodular lattice points that fall into a dilated and translated parallelogram. By using an article from Skriganov, we see that this error can be compared to an ergodic sum that involves the discrete…

This preprint is a text for students and teachers on inequalities. Some standard topics are covered on application of calculus to inequality proving. Many examples are considered, stated, solved or partially solved. Some problems are…

Central limit theorems (CLTs) have a long history in probability and statistics. They play a fundamental role in constructing valid statistical inference procedures. Over the last century, various techniques have been developed in…

A new error bound for the linear complementarity problem when the matrix involved is a B-matrix is presented, which improves the corresponding result in [C.Q. Li et al., A new error bound for linear complementarity problems for B-matrices.…

We improve the error term in the van der Corput transform for exponential sums \sum_{a \le n \le b} g(n) exp(2\pi i f(n)). For many functions g and f, we can extract the next term in the asymptotic, showing that previous results, such as…

We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when…

We use classical methods from analytic number theory to resolve the lattice point counting problem on the first Heisenberg group, in the case where the gauge function is taken to be the Cygan-Kor$\acute{a}$nyi Heisenberg-norm…

This paper is a corrigendum to the article 'On the ideal theorem for number fields`. The main result of this paper proves to be untrue and is replaced by an estimate of a weighted sum with an improved error term.

To avoid instabilities in the continuum semi-classical limit of loop quantum cosmology models, refinement of the underlying lattice is necessary. The lattice refinement leads to new dynamical difference equations which, in general, do not…

We study different extended formulations for the set $X = \{x\in\mathbb{Z}^n \mid Ax = Ax^0\}$ in order to tackle the feasibility problem for the set $X_+=X \cap \mathbb{Z}^n_+$. Here the goal is not to find an improved polyhedral…

This research concerns the estimation of latent linear or polychoric correlations from fuzzy frequency tables. Fuzzy counts are of particular interest to many disciplines including social and behavioral sciences, and are especially relevant…

We give an explicit upper bound on the volume of lattice simplices with fixed positive number of interior lattice points. The bound differs from the conjectural sharp upper bound only by a linear factor in the dimension. This improves…

We consider the problem of counting lattice points contained in domains in $\mathbb{R}^d$ defined by products of linear forms and we show that the normalized discrepancies in these counting problems satisfy non-degenerate Central Limit…

We describe a systematic expansion for full QCD. The leading term in the expansion gives the valence approximation. The expansion reproduces full QCD if an infinite number of higher terms are included.

We prove explicit bounds on the number of lattice points on or near a convex curve in terms of geometric invariants such as length, curvature, and affine arclength. In several of our results we obtain the best possible constants. Our…

Progress on the calculation of the spectrum from lattice calculations is reviewed. Particular emphasis is placed on discussing our ability to control possible systematic errors coming from finite volume, and extrapolations in quark mass and…