A converse to linear independence criteria, valid almost everywhere

Jason Levesley; Simon Kristensen; Mumtaz Hussain; Stéphane Fischler

doi:10.1007/s11139-014-9662-8

A converse to linear independence criteria, valid almost everywhere

Jason Levesley, Simon Kristensen, Mumtaz Hussain, Stéphane Fischler

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove a weighted analogue of the Khintchine-Groshev Theorem, where the distance to the nearest integer is replaced by the absolute value. This is subsequently applied to proving the optimality of several linear independence criteria over the field of rational numbers.

Original language	English
Number of pages	11
Journal	The Ramanujan Journal
Early online date	24 Jan 2015
DOIs	https://doi.org/10.1007/s11139-014-9662-8
Publication status	Published - 2015

Access to Document

10.1007/s11139-014-9662-8

http://arxiv.org/abs/1302.1952

Cite this

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title = "A converse to linear independence criteria, valid almost everywhere",

abstract = "We prove a weighted analogue of the Khintchine-Groshev Theorem, where the distance to the nearest integer is replaced by the absolute value. This is subsequently applied to proving the optimality of several linear independence criteria over the field of rational numbers.",

author = "Jason Levesley and Simon Kristensen and Mumtaz Hussain and St{\'e}phane Fischler",

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AU - Kristensen, Simon

AU - Hussain, Mumtaz

AU - Fischler, Stéphane

PY - 2015

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AB - We prove a weighted analogue of the Khintchine-Groshev Theorem, where the distance to the nearest integer is replaced by the absolute value. This is subsequently applied to proving the optimality of several linear independence criteria over the field of rational numbers.

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DO - 10.1007/s11139-014-9662-8

M3 - Article

JO - The Ramanujan Journal

JF - The Ramanujan Journal

ER -