Waring’s problem for Beatty sequences and a local to global principle
William D. Banks1; Ahmet M. Güloğlu2; Robert C. Vaughan3
1 Department of Mathematics University of Missouri Columbia, MO 65211 USA
2 Department of Mathematics Bilkent University 06800 Bilkent, Ankara, TURKEY
3 Department of Mathematics Pennsylvania State University University Park, PA 16802-6401 USA
Journal de théorie des nombres de Bordeaux, Volume 26 (2014) no. 1, pp. 1-16.

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.

Nous examinons de façons diverses la représentation d’un grand nombre entier N comme somme de s entiers positifs qui sont tous des puissances k-ième de termes d’une suite de Beatty donnée. Entre autres, une forme très générale du principe local-global est établie dans la théorie additive des nombres. La démonstration est courte mais elle utilise un théorème profond de M. Kneser.

DOI: 10.5802/jtnb.855
Classification: 11P05

William D. Banks 1; Ahmet M. Güloğlu 2; Robert C. Vaughan 3

1 Department of Mathematics University of Missouri Columbia, MO 65211 USA
2 Department of Mathematics Bilkent University 06800 Bilkent, Ankara, TURKEY
3 Department of Mathematics Pennsylvania State University University Park, PA 16802-6401 USA 
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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, Volume 26 (2014) no. 1, pp. 1-16. doi : 10.5802/jtnb.855. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.855/

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