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WARING’S PROBLEM WITH PIATETSKI-SHAPIRO NUMBERS

Part of: Exponential sums and character sums Sequences and sets Additive number theory; partitions

Published online by Cambridge University Press:  17 February 2016

Yıldırım Akbal  and
Ahmet M. Güloğlu
Yıldırım Akbal
Affiliation:
Department of Mathematics, Bilkent University, 06800 Bilkent, Ankara, Turkey email yildirim.akbal@bilkent.edu.tr
Ahmet M. Güloğlu
Affiliation:
Department of Mathematics, Bilkent University, 06800 Bilkent, Ankara, Turkey email guloglua@fen.bilkent.edu.tr
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Abstract

In this paper, we investigate in various ways the representation of a large natural number as a sum of a fixed power of Piatetski-Shapiro numbers, thereby establishing a variant of the Hilbert–Waring problem with numbers from a sparse sequence.

MSC classification

Primary: 11P05: Waring's problem and variants
Secondary: 11P55: Applications of the Hardy-Littlewood method 11L07: Estimates on exponential sums 11L15: Weyl sums 11B83: Special sequences and polynomials
Type
Research Article
Information
Mathematika , Volume 62 , Issue 2 , 2016 , pp. 524 - 550
Copyright
Copyright © University College London 2016 

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