Waring’s problem for Beatty sequences and a local to global principle
Journal de Théorie des Nombres de Bordeaux, Tome 26 (2014) no. 1, pp. 1-16.

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.

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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DOI : https://doi.org/10.5802/jtnb.855
Classification : 11P05
@article{JTNB_2014__26_1_1_0,
     author = {William D. Banks and Ahmet M. G\"ulo\u{g}lu and Robert~C. Vaughan},
     title = {Waring{\textquoteright}s problem for {Beatty} sequences and a local to global principle},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {1--16},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {26},
     number = {1},
     year = {2014},
     doi = {10.5802/jtnb.855},
     mrnumber = {3232763},
     zbl = {1303.11110},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.855/}
}
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, Tome 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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