Liminf Sets in Simultaneous Diophantine Approximation | Zendy

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Liminf Sets in Simultaneous Diophantine Approximation

Author(s) -

Faustin Adiceam

Publication year - 2016

Publication title -

journal de théorie des nombres de bordeaux

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.663

H-Index - 26

eISSN - 2118-8572

pISSN - 1246-7405

DOI - 10.5802/jtnb.949

Subject(s) - mathematics , rational number , complement (music) , hausdorff dimension , diophantine equation , diophantine approximation , set (abstract data type) , combinatorics , discrete mathematics , real number , tuple , number theory , diophantine set , hausdorff space , biochemistry , chemistry , complementation , computer science , programming language , gene , phenotype

Let Q be an infinite set of positive integers. Denote by W(Q) the set of n-tuples of real numbers simultaneously tau-well approximable by infinitely many rationals with denominators in Q but only by finitely many rationals with denominators in the complement of Q. The Hausdorff dimension of the liminf set W(Q) is computed when tau > 2 + 1/n. A p-adic analogue of the problem is also studied.

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