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DIOPHANTINE TRANSFERENCE PRINCIPLE OVER FUNCTION FIELDS

Part of: Probabilistic theory: distribution modulo $1$; metric theory of algorithms Ergodic theory Diophantine approximation, transcendental number theory Dynamical systems with hyperbolic behavior Lie groups

Published online by Cambridge University Press:  28 February 2024

SOURAV DAS Open the ORCID record for SOURAV DAS [Opens in a new window]  and
ARIJIT GANGULY Open the ORCID record for ARIJIT GANGULY [Opens in a new window]
SOURAV DAS*
Affiliation:
Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur 208016, India
ARIJIT GANGULY
Affiliation:
Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur 208016, India e-mail: arijit.ganguly1@gmail.com
*
e-mail: iamsouravdas1@gmail.com
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Abstract

We study the Diophantine transference principle over function fields. By adapting the approach of Beresnevich and Velani [‘An inhomogeneous transference principle and Diophantine approximation’, Proc. Lond. Math. Soc. (3) 101 (2010), 821–851] to function fields, we extend many results from homogeneous to inhomogeneous Diophantine approximation. This also yields the inhomogeneous Baker–Sprindžuk conjecture over function fields and upper bounds for the general nonextremal scenario.

Keywords

inhomogeneous Diophantine approximationtransference principledynamical systems

MSC classification

Primary: 11J61: Approximation in non-Archimedean valuations
Secondary: 11J83: Metric theory 22E40: Discrete subgroups of Lie groups 11K60: Diophantine approximation 37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 37A17: Homogeneous flows
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 18
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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