Related papers: Variance of Lattice Point Counting in Thin Annuli

Asymptotics are given for the number of rational points in the domain of a morphism of weighted projective stacks whose images have bounded height and satisfy a (possibly infinite) set of local conditions. As a consequence we obtain results…

We derive the local and central limit theorems for the Stirling numbers of the second kind by elementary means, obtaining as corollaries effective asymptotic estimates for the Bell numbers and for the moments of the distribution. We also…

A method is presented for estimating the background at a given location on a sky map by interpolating the estimated background from a set of concentric annuli which surround this location. If the background is nonuniform but smoothly…

We investigate the structure of branching asymptotics appearing in solutions to elliptic edge problems. The exponents in powers of the half-axis variable, logarithmic terms, and coefficients depend on the variables on the edge and may be…

We investigate the asymptotic density of error-correcting codes with good distance properties and prescribed linearity degree, including sublinear and nonlinear codes. We focus on the general setting of finite translation-invariant metric…

We study the asymptotic density of the set of subscripts of the Bernoulli numbers having a given denominator. We also study the distribution of distinct Bernoulli denominators and some related problems.

We produce embeddings of knots in thin position that admit compressible thin levels. We also find the bridge number of tangle sums where each tangle is high distance.

Counting integer points in large convex bodies with smooth boundaries containing isolated flat points is oftentimes an intermediate case between balls (or convex bodies with smooth boundaries having everywhere positive curvature) and cubes…

Asymptotics are derived for the scaling of the total diffraction intensity for the set of $k$-free integers near the origin, which is a measure for the degree of patch fluctuations.

For noninteracting particles moving in a Gaussian random potential, there exists a disagreement in the literature on the asymptotic expression for the density of states in the tail of the band. We resolve this discrepancy. Further we…

We give a survey of work on the number of vertices of the convex hull of integer points defined by the system of linear inequalities. Also, we present our improvement of some of these.

We present a method for finding the asymptotics of integrals arising in solid mechanics.

We derive an asymptotic expansion for two-dimensional displacement field associated to thin elastic inhomogeneities having no uniform thickness. Our derivation is rigorous and based on layer potential techniques. We extend these techniques…

We enumerate the intervals in the Tamari lattices. For this, we introduce an inductive description of the intervals. Then a notion of "new interval" is defined and these are also enumerated. A a side result, the inverse of two special…

We provide an asymptotic estimate for the number of rational points of bounded height on a non-singular conic over the rationals. The estimate is uniform in the coefficients of the underlying quadratic form.

We exhibit a procedure to asymptotically enumerate monotone grid classes of permutations. This is then applied to compute the asymptotic number of permutations in any connected one-corner class. Our strategy consists of enumerating the…

Inspired by the complexity of certain real-world datasets, this article introduces a novel flexible linear spline index regression model. The model posits piecewise linear effects of an index on the response, with continuous changes…

Consider a convex body $C \subset \mathbb{R}^d$. Let $X$ be a random point with uniform distribution in $[0,1]^d$. Consider the value $X_C$ equal to the number of lattice points $\mathbb Z^d$ inside the body $C$ shifted by $X$. It is well…

Orders in number fields provide natural examples of lattices. We ask: what can the successive minima of lattices arising from orders in number fields be? Given an order $\mathcal{O}$ of absolute discriminant $\Delta$ in a degree $n$ number…

In this note we give a combinatorial and non-computational proof of the asymptotics of the integer moments of the moments of the characteristic polynomials of Haar distributed unitary matrices as the size of the matrix goes to infinity.…