FULLY INHOMOGENEOUS MULTIPLICATIVE DIOPHANTINE APPROXIMATION OF BADLY APPROXIMABLE NUMBERS | Zendy

Chow Sam | Zendy; Zafeiropoulos Agamem | Zendy

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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 .

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