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A NOTE ON WEIGHTED BADLY APPROXIMABLE LINEAR FORMS

Part of: Diophantine approximation, transcendental number theory Probabilistic theory: distribution modulo $1$; metric theory of algorithms

Published online by Cambridge University Press:  10 June 2016

STEPHEN HARRAP  and
NIKOLAY MOSHCHEVITIN
STEPHEN HARRAP
Affiliation:
Department of Mathematical Sciences, Science Laboratories, Durham University, South Rd, Durham, DH1 3LE, United Kingdom e-mail: s.g.harrap@durham.ac.uk
NIKOLAY MOSHCHEVITIN
Affiliation:
Department of Mathematics and Mechanics, Moscow State University, Leninskie Gory 1, GZ MGU, 119991 Moscow, Russia e-mail: moshchevitin@rambler.ru
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Abstract

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We prove a result in the area of twisted Diophantine approximation related to the theory of Schmidt games. In particular, under certain restrictions we give an affirmative answer to the analogue in this setting of a famous conjecture of Schmidt from Diophantine approximation.

MSC classification

Primary: 11J83: Metric theory
Secondary: 11J13: Simultaneous homogeneous approximation, linear forms 11K60: Diophantine approximation

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 59 , Issue 2 , May 2017 , pp. 349 - 357
Copyright
Copyright © Glasgow Mathematical Journal Trust 2016 

References

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