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FULLY INHOMOGENEOUS MULTIPLICATIVE DIOPHANTINE APPROXIMATION OF BADLY APPROXIMABLE NUMBERS
Author(s) -
Chow Sam,
Zafeiropoulos Agamem
Publication year - 2021
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/mtk.12095
Subject(s) - mathematics , diophantine approximation , assertion , multiplicative function , conjecture , set (abstract data type) , combinatorics , line (geometry) , diophantine equation , mathematical analysis , geometry , computer science , programming language
We establish a strong form of Littlewood's conjecture with inhomogeneous shifts, for a full‐dimensional set of pairs of badly approximable numbers on a vertical line. We also prove a uniform assertion of this nature, generalising a strong form of a result of Haynes et al . Finally, we establish a similar result involving inhomogeneously badly approximable numbers, making progress towards a problem posed by Pollington et al .