Related papers: Extremal numbers and multi-parametric geometry of …

The papers shows an algorithm to search for approximations of reals to rationals of the form a/b^2 that runs on \sqrt(b) polynomial time steps.

In this paper,we count the rational points on the weighted projective spaces defined over number fields w.r.t. ``size''. An asymptotic formula which generalizes the result of Schanuel's ``Heights in number fields'' is obtained. Furthermore,…

We compute the constant of approximation for an arbitrary rational point on an arbitrary smooth cubic hypersurface $X$ over a number field $k$, provided that there is a $k$-rational line somewhere on $X$. In the process, we verify the Coba…

For a fixed set $X$, an arbitrary \textit{weight structure} $d \in [0,\infty]^{X \times X}$ can be interpreted as a distance assignment between pairs of points on $X$. Restrictions (i.e. \textit{metric axioms}) on the behaviour of any such…

Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms.…

We study balls of homogeneous cubics on $\mathbb R^n$, $n = 2,3$, which are bounded by unity on the unit sphere. For $n = 2$ we completely describe the facial structure of this norm ball, while for $n = 3$ we classify all extremal points…

Let $X$ be a finite, 2-dimensional cell complex. The curvature invariants $\rho_\pm(X)$ and $\sigma_\pm(X)$ were defined in [13], and a programme of conjectures was outlined. Here, we prove the foundational result that the quantities…

Uniform convergence rates are provided for asymptotic representations of sample extremes. These bounds which are universal in the sense that they do not depend on the extreme value index are meant to be extended to arbitrary samples…

We prove asymptotic formulas for the number of rational points of bounded height on certain blow-ups of the projective space.

In this note we give exact formulas (and asymptotics) for the number of rational points of bounded height on weighted projective stacks over global function fields.

We investigate the enumerative geometry of point configurations in projective space. We define "projective configuration counts": these enumerate configurations of points in projective space such that certain specified subsets are in fixed…

The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…

Proper continued fractions are generalized continued fractions with positive integer numerators $a_i$ and integer denominators with $b_i\geq a_i$. In this paper we study the strength of approximation of irrational numbers to their…

The goal of this paper is to generalize the main results of [KM] and subsequent papers on metric Diophantine approximation with dependent quantities to the set-up of systems of linear forms. In particular, we establish `joint strong…

This paper considers extreme values attained by a centered, multidimensional Gaussian process $X(t)= (X_1(t),\ldots,X_n(t))$ minus drift $d(t)=(d_1(t),\ldots,d_n(t))$, on an arbitrary set $T$. Under mild regularity conditions, we establish…

We prove some sharp extremal distance results for functions in weighted Bergman spaces on the upper halfplane.We also prove such results in the context of bounded strictly pseudoconvex domains with smooth boundary

We study the interaction between the group law on an elliptic curve and the additive structure of $x$-coordinates of rational points on an elliptic curve. Let $E/\mathbb{Q}$ be an elliptic curve of Mordell-Weil rank $r \geq 1$, $d \geq 1$…

We give a numerical characterization of the possible extremal Betti numbers (values as well as positions) of any homogeneous ideal in a polynomial ring over a field.

This paper is devoted to Markov's extremal problems of the form $M_{n,k}=\sup_{p\in\PP_n\setminus\{0\}}{{\|p^{(k)}\|}_X}/{{\|p\|}_X}$ $(1\le k\le n)$, where $\PP_n$ is the set of all algebraic polynomials of degree at most $n$ and $X$ is a…

The paper describes a simple deterministic parallel/distributed (2+epsilon)-approximation algorithm for the minimum-weight vertex-cover problem and its dual (edge/element packing).