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  • 2003.10161v1

    Accepted author manuscript, 486 KB, PDF document

    Available under license: CC BY: Creative Commons Attribution 4.0 International License

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Counting monochromatic solutions to diagonal Diophantine equations

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>23/03/2020
<mark>Journal</mark>arXiv
Publication StatusPublished
<mark>Original language</mark>English

Abstract

Given a finite colouring of the positive integers, we count monochromatic solutions to a variety of Diophantine equations, each of which can be written by setting a diagonal quadratic form equal to a linear form. As a consequence, we determine an algebraic criterion for when such equations are partition regular. Our methods involve discrete harmonic analysis and require a number of `mixed' restriction estimates, which may be of independent interest.