Results 21 to 30 of about 2,483 (259)
Independence Inheritance and Diophantine Approximation for Systems of Linear Forms [PDF]
International mathematics research notices, 2021 The classical Khintchine–Groshev theorem is a generalization of Khintchine’s theorem on simultaneous Diophantine approximation, from approximation of points in ${\mathbb {R}}^m$ to approximation of systems of linear forms in ${\mathbb {R}}^{nm}$.
D. Allen, F. Ramírez
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Diophantine Approximation in Metric Space [PDF]
, 2021 Diophantine approximation is traditionally the study of how well real numbers are approximated by rationals. We propose a model for studying Diophantine approximation in an arbitrary totally bounded metric space where the rationals are replaced with a ...
Ramírez, Felipe A. +2 more
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Intrinsic Diophantine approximation for overlapping iterated function systems [PDF]
Mathematische Annalen, 2021 In this paper we study a family of limsup sets that are defined using iterated function systems. Our main result is an analogue of Khintchine’s theorem for these sets.
S. Baker
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Mahler’s question for intrinsic Diophantine approximation on triadic Cantor set: the divergence theory [PDF]
Mathematische Zeitschrift, 2021 In this paper, we consider Mahler’s question for intrinsic Diophantine approximation on the triadic Cantor set K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy ...
Bo Tan, Bao-Wei Wang, Jun Wu
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On the Approximation of Quasiperiodic Functions with Diophantine Frequencies by Periodic Functions [PDF]
SIAM Journal on Mathematical Analysis, 2023 We present an analysis of the approximation error for a $d$-dimensional quasiperiodic function $f$ with Diophantine frequencies, approximated by a periodic function with the fundamental domain $[0,L_1)\times [0,L_2)\times \cdots \times[0,L_d)$.
Kai Jiang, Shifeng Li, Pingwen Zhang
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On Hausdorff dimension in inhomogeneous Diophantine approximation over global function fields [PDF]
Journal of Number Theory, 2021 In this paper, we study inhomogeneous Diophantine approximation over the completion $K_v$ of a global function field $K$ (over a finite field) for a discrete valuation $v$, with affine algebra $R_v$.
Taehyeong Kim, Seonhee Lim, F. Paulin
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Simultaneous p-adic Diophantine approximation [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2021 The aim of this paper is to develop the theory of weighted Diophantine approximation of rational numbers to p-adic numbers. Firstly, we establish complete analogues of Khintchine’s theorem, the Duffin–Schaeffer theorem and the Jarník–Besicovitch theorem ...
V. Beresnevich +2 more
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Linear Diophantine Fuzzy Rough Sets on Paired Universes with Multi Stage Decision Analysis
Axioms, 2022 Rough set (RS) and fuzzy set (FS) theories were developed to account for ambiguity in the data processing. The most persuasive and modernist abstraction of an FS is the linear Diophantine FS (LD-FS).
Saba Ayub +5 more
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Weighted uniform Diophantine approximation of systems of linear forms [PDF]
Pure and Applied Mathematics Quarterly, 2021 Following the development of weighted asymptotic approximation properties of matrices, we introduce the analogous uniform approximation properties (that is, study the improvability of Dirichlet's Theorem).
D. Kleinbock, Anurag Rao
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Журнал Белорусского государственного университета: Математика, информатика, 2021 The article is devoted to the latest results in metric theory of Diophantine approximation. One of the first major result in area of number theory was a theorem by academician Jonas Kubilius. This paper is dedicated to centenary of his birth.
Victor V. Beresnevich +4 more
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