相关论文: Arithmetic Fujita approximation
We show that a simple and straightforward rational approximation to the Thomas--Fermi equation provides the slope at origin with unprecedented accuracy. We compare present approach with other available ones.
We show that any big line bundle on a smooth projective variety admits a special Fujita approximation: the volume and the first Riemann-Roch coefficient are both approximated by those of ample $\mathbb{Q}$-line bundles on higher models.…
We obtain matching direct and inverse theorems for the degree of weighted $L_p$-approximation by polynomials with the Jacobi weights $(1-x)^\alpha (1+x)^\beta$. Combined, the estimates yield a constructive characterization of various…
This expository article proves some results of Ferguson, on the approximation of continuous functions on a compact subset of R by polynomials with integral coefficients.
We present a proof of the folklore result that any length metric on $\mathbb R^d$ can be approximated by conformally flat Riemannian distance functions in the uniform distance. This result is used to study Liouville quantum gravity in…
We give a proof of a phenomenon conjectured in our former article: "Beltrami forms, affine surfaces and the Schwarz-Christoffel formula: a worked out example of straightening". We also start an abstract discussion of the notion of limits of…
We continue with our study of the arithmetic geometry of toric varieties. In this text, we study the positivity properties of metrized R-divisors in the toric setting. For a toric metrized R-divisor, we give formulae for its arithmetic…
These notes are devoted to a detailed exposition of the proof of the Geometric Satake Equivalence for general coefficients, following Mirkovic-Vilonen.
We prove a sharp analogue of Minkowski's inhomogeneous approximation theorem over fields of power series $\mathbb{F}_q((T^{-1}))$. Furthermore, we study the approximation to a given point $\underline{y}$ in $\mathbb{F}_q((T^{-1}))^2$ by the…
In this note, we determined the distance signatures of the incidence matrices of affine resolvable designs. This proves a conjecture by Kohei Yamada.
By using the $\mathbb R$-filtration approach of Arakelov geometry, one establishes explicit upper bounds for geometric and arithmetic Hilbert-Samuel function for line bundles on projective varieties and hermitian line bundles on arithmetic…
A conjecture of Orlov predicts that derived equivalent smooth projective varieties over a field have isomorphic Chow motives. The conjecture is known for curves, and was recently observed for surfaces by Huybrechts. In this paper we focus…
We prove a "discrete analogue" for Taelman's class modules of certain Conjectures formulated by R. Greenberg for cyclotomic fields.
In this paper we show how to construct inner and outer convex approximations of a polytope from an approximate cone factorization of its slack matrix. This provides a robust generalization of the famous result of Yannakakis that polyhedral…
In this paper, we construct certain analogues of the Arakawa-Kaneko zeta functions. We prove functional relations between these functions and the Mordell-Tornheim multiple zeta functions. Furthermore we give some formulas among…
We extend Fukushima's result on the finite convergence of an algorithm for the global convex feasibility problem to the local nonconvex case.
Approximable algebras were defined by Chen in his proof of the Fujita theorem in the arithmetic context. These were shown to not be necessarily subalgebras of section rings of big line bundles in a previous prepreint of the author. Here, we…
We present Korovkin approximation theorems that incorporate summability methods. These result allows us to obtain a unified treatment of several previous results, focusing on the underlying structure and the properties that a summability…
We investigate a function field analogue of a recent conjecture on autocorrelations of sums of two squares by Freiberg, Kurlberg and Rosenzweig, which generalizes an older conjecture by Connors and Keating. In particular, we provide…
We present an approximation version of the results of D. P. Gupta [ J. of Approx. Theory, 7 (1973), 226-238] A. N. S. Singroura [Proc. Japan Acad., 39 (4) (1963), 208-210] and G. Szeg\"{o} [Math. Z., 25 (1926), 87-115]. Some corollaries and…