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

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

Journal de Théorie des Nombres de Bordeaux (2014)

  • Volume: 26, Issue: 1, page 1-16
  • ISSN: 1246-7405

Abstract

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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.

How to cite

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Banks, William D., Güloğlu, Ahmet M., and Vaughan, Robert C.. "Waring’s problem for Beatty sequences and a local to global principle." Journal de Théorie des Nombres de Bordeaux 26.1 (2014): 1-16. <http://eudml.org/doc/275796>.

@article{Banks2014,
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.},
affiliation = {Department of Mathematics University of Missouri Columbia, MO 65211 USA; Department of Mathematics Bilkent University 06800 Bilkent, Ankara, TURKEY; Department of Mathematics Pennsylvania State University University Park, PA 16802-6401 USA},
author = {Banks, William D., Güloğlu, Ahmet M., Vaughan, Robert C.},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Waring's problem; Beatty sequence; Hardy-Littlewood method},
language = {eng},
month = {4},
number = {1},
pages = {1-16},
publisher = {Société Arithmétique de Bordeaux},
title = {Waring’s problem for Beatty sequences and a local to global principle},
url = {http://eudml.org/doc/275796},
volume = {26},
year = {2014},
}

TY - JOUR
AU - Banks, William D.
AU - Güloğlu, Ahmet M.
AU - Vaughan, Robert C.
TI - Waring’s problem for Beatty sequences and a local to global principle
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2014/4//
PB - Société Arithmétique de Bordeaux
VL - 26
IS - 1
SP - 1
EP - 16
AB - 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.
LA - eng
KW - Waring's problem; Beatty sequence; Hardy-Littlewood method
UR - http://eudml.org/doc/275796
ER -

References

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  15. R. C. Vaughan and T. D. Wooley, Further improvements in Waring’s problem. Acta Math. 174 (1995), no. 2, 147–240. Zbl0849.11075MR1351319
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  18. T. D. Wooley, Vinogradov’s mean value theorem via efficient congruencing. Ann. Math., to appear. Zbl1267.11105MR3039678

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