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December 2008 Additive Representation in Thin Sequences, VII: Restricted Moments of the Number of Representations
Jörg Brüdern, Koichi Kawada, Trevor D. Wooley
Tsukuba J. Math. 32(2): 383-406 (December 2008). DOI: 10.21099/tkbjm/1496165237

Abstract

Let $R_{s,k}(n)$ denote the number of representations of $n$ as the sum of $s$ positive integral $k$th powers. We develop methods to establish asymptotic formulae for moments of $R_{s,k}(n)$ in which $n$ is restricted to a thin sequence consisting of values of a given polynomial. As a first example, we discuss the case of cubes, and present conclusions for sums of 6 and 7 cubes in which the polynomial is quadratic, and for sums of 7 cubes in which the polynomial is cubic. We also consider the case wherein the exponent $k$ is large, and briefly describe corresponding results for the binary Goldbach problem.

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Jörg Brüdern. Koichi Kawada. Trevor D. Wooley. "Additive Representation in Thin Sequences, VII: Restricted Moments of the Number of Representations." Tsukuba J. Math. 32 (2) 383 - 406, December 2008. https://doi.org/10.21099/tkbjm/1496165237

Information

Published: December 2008
First available in Project Euclid: 30 May 2017

zbMATH: 1183.11059
MathSciNet: MR2477988
Digital Object Identifier: 10.21099/tkbjm/1496165237

Rights: Copyright © 2008 University of Tsukuba, Institute of Mathematics

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Vol.32 • No. 2 • December 2008
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