- Title
- A note on the weighted Khintchine-Groshev Theorem
- Creator
- Hussain, Mumtaz; Yusupova, Tatiana
- Relation
- ARC
- Relation
- Journal de Theorie des Nombres de Bordeaux Vol. 26, Issue 2, p. 385-397
- Relation
- http://math.au.dk/publs?publid=977
- Publisher
- Universite de Bordeaux I * Centre de Recherces en Mathematiques
- Resource Type
- journal article
- Date
- 2014
- Description
- Let W(m,n;̲ψ) denote the set of ψ₁,…,ψn-approximable points in Rmn. The classical Khintchine-Groshev theorem assumes a monotonicity condition on the approximating functions ̲ψ. Removing monotonicity from the Khintchine-Groshev theorem is attributed to different authors for different cases of m and n. It can not be removed for m=n=1 as Duffin-Shcaeffer provided the counter example. We deal with the only remaining case m=2 and thereby remove all unnecessary conditions from the Khintchine-Groshev theorem.
- Subject
- Khintchine-Groshev; theorem; monotonicity condition; variables
- Identifier
- http://hdl.handle.net/1959.13/1067884
- Identifier
- uon:18507
- Identifier
- ISSN:1246-7405
- Language
- eng
- Reviewed
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