Göteborgs universitets publikationer

# On m-covering families of Beatty sequences with irrational moduli

Författare och institution:
Peter Hegarty (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU)
Journal of Number Theory, 132 ( 10 ) s. 2277-2296
ISSN:
0022-314X
Publikationstyp:
Publiceringsår:
2012
Språk:
engelska
Fulltextlänk:
Sammanfattning (abstract):
We generalise Uspensky's theorem characterising eventual exact (e.e.) covers of the positive integers by homogeneous Beatty sequences, to e.e. m-covers, for any m \in \N, by homogeneous sequences with irrational moduli. We also consider inhomogeneous sequences, again with irrational moduli, and obtain a purely arithmetical characterisation of e.e. m-covers. This generalises a result of Graham for m = 1, but when m > 1 the arithmetical description is more complicated. Finally we speculate on how one might make sense of the notion of an exact m-cover when m is not an integer, and present a "fractional version" of Beatty's theorem.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik ->
Annan matematik
Nyckelord:
Beatty sequence, Weyl criterion
Chalmers fundament:
Grundläggande vetenskaper
Postens nummer:
159181