Related papers: Arithmetic Fujita approximation

Using an alternative notion of good reduction, an analog of the Shafarevich theorem for elliptic curves is proved for morphisms of the projective line over number fields.

We extend the results of Xh. Z. Krasniqi [Acta Comment. Univ. Tartu. Math. 17 (2013), 89-101] and the authors [Acta Comment. Univ. Tartu. Math. 13 (2009), 11-24]. to the case where in the measures of estimations there are used…

We generalize Dirichlet's diophantine approximation theorem to approximating any real number $\alpha$ by a sum of two rational numbers $\frac{a_1}{q_1} + \frac{a_2}{q_2}$ with denominators $1 \leq q_1, q_2 \leq N$. This turns out to be…

A. Poltotaski proved an analog of Carleson's Theorem on almost everywhere convergence of Fourier series for a version of the non-linear Fourier transform. We aim to present his proof in full detail and elaborate on the ideas behind each…

We recall two approaches to recent improvements of the classical Sobolev inequality. The first one follows the point of view of Real Analysis, while the second one relies on tools from Convex Geometry. In this paper we prove a (sharp)…

We give an elementary geometric proof using Ford circles that the convergents of the continued fraction expansion of a real number $\alpha$ coincide with the rationals that are best approximations of the second kind of $\alpha$.

This article provides a power series summability based Korovkin type approximation theorem for any fuzzy sequence of positive linear operators. Using the notion of fuzzy modulus of smoothness, we also derive an associated approximation…

Using the theory of moduli of curves, we establish various slope inequalities for general fibered surfaces. More precisely, we introduce the notion of functorial divisors on Artin stacks and prove a theorem concerning their effectiveness.…

The affine Yangian of $\mathfrak{gl}_1$ has recently appeared simultaneously in the work of Maulik-Okounkov and Schiffmann-Vasserot in connection with the Alday-Gaiotto-Tachikawa conjecture. While the former presentation is purely…

Mirror symmetry relates Gromov-Witten invariants of an elliptic curve with certain integrals over Feynman graphs. We prove a tropical generalization of mirror symmetry for elliptic curves, i.e., a statement relating certain labeled…

We prove some generalizations of the sum formula for multiple zeta values by using Hiroyuki Ochiai's method of proving the sum formula.

A multidimesional function $y(\vec r)$ defined by a sample of points $\{\vec r_i,y_i\}$ is approximated by a differentiable function $\widetilde y(\vec r)$. The problem is solved by using the Gauss-Hermite folding method developed in the…

We prove a Torelli-like theorem for higher-dimensional function fields, from the point of view of "almost-abelian" anabelian geometry.

Suppose that $\ff \in \reals^{n}$ is a vector of $n$ error-contaminated measurements of $n$ smooth values measured at distinct and strictly ascending abscissae. The following projective technique is proposed for obtaining a vector of smooth…

Buan-Iyama-Reiten-Smith proved, based on Derksen-Weyman-Zelevinsky work, that the Jacobian algebra of two quivers with potential related by a QP-mutation are nearly Morita equivalent. They proved, using Axiom of Choice, that the natural…

The classical Artin--Whaples approximation theorem allows to simultaneously approximate finitely many different elements of a field with respect to finitely many pairwise inequivalent absolute values. Several variants and generalizations…

Under an infinitesimal version of the Bishop-Gromov relative volume comparison condition for a measure on an Alexandrov space, we prove a topological splitting theorem of Cheeger-Gromoll type. As a corollary, we prove an isometric splitting…

The purpose of this book is to build up the fundament of an Arakelov theory over adelic curves in order to provide a unified framework for the researches of arithmetic geometry in several directions.

Let $A$ be a subset of a finite field $F := \Z/q\Z$ for some prime $q$. If $|F|^\delta < |A| < |F|^{1-\delta}$ for some $\delta > 0$, then we prove the estimate $|A+A| + |A.A| \geq c(\delta) |A|^{1+\eps}$ for some $\eps = \eps(\delta) > 0$.…

Approximative properties of linear summation methods of Fourier series are considered in the Orlicz type spaces ${\mathcal S}_{M}$. In particular, in terms of approximations by such methods, constructive characteristics are obtained for…