Waring's problem for Beatty sequences and a local to global principle

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 d...

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Veröffentlicht in:	Journal de theorie des nombres de bordeaux 2014-01, Vol.26 (1), p.1-16
Hauptverfasser:	BANKS, William D., GÜLOĞLU, Ahmet M., VAUGHAN, Robert C.
Format:	Artikel
Sprache:	eng
Schlagworte:	College mathematics Integers Mathematical congruence Mathematical sequences Mathematical theorems Natural numbers Number theory Real numbers
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creator	BANKS, William D. GÜLOĞLU, Ahmet M. VAUGHAN, Robert C.
description	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.
doi_str_mv	10.5802/jtnb.855
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subjects	College mathematics Integers Mathematical congruence Mathematical sequences Mathematical theorems Natural numbers Number theory Real numbers
title	Waring's problem for Beatty sequences and a local to global principle
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