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ON WARING’S PROBLEM IN SUMS OF THREE CUBES FOR SMALLER POWERS

Part of: Additive number theory; partitions

Published online by Cambridge University Press:  16 September 2021

JAVIER PLIEGO
JAVIER PLIEGO*
Affiliation:
Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907-2067, USA e-mail: jpliegog@purdue.edu and School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol, BS8 1UG, UK
*
e-mail: jp17412@bristol.ac.uk
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Abstract

We give an upper bound for the minimum s with the property that every sufficiently large integer can be represented as the sum of s positive kth powers of integers, each of which is represented as the sum of three positive cubes for the cases $2\leq k\leq 4.$

Keywords

Waring’s problemHardy–Littlewood method

MSC classification

Primary: 11P05: Waring's problem and variants
Secondary: 11P55: Applications of the Hardy-Littlewood method
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 114 , Issue 3 , June 2023 , pp. 378 - 405
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by D. Badziahin

The author’s work was supported in part by a European Research Council Advanced Grant under the European Union’s Horizon 2020 research and innovation programme via grant agreement no. 695223 during his studies at the University of Bristol.

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