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William D. Banks; Ahmet M. Güloğlu; Robert C. Vaughan
Waring’s problem for Beatty sequences and a local to global principle
Journal de théorie des nombres de Bordeaux, 26 no. 1 (2014), p. 1-16, doi: 10.5802/jtnb.855
Article PDF | Reviews MR 3232763 | Zbl 06304177
Class. Math.: 11P05

Résumé - Abstract

We investigate in various ways the representation of a large natural number $N$ as a sum of $s$ positive $k$-th powers of numbers from a fixed Beatty sequence. Inter alia, a very general form of the local to global principle is established in additive number theory. Although the proof is very short, it depends on a deep theorem of M. Kneser.

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