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Counting monochromatic solutions to diagonal Diophantine equations

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Counting monochromatic solutions to diagonal Diophantine equations. / Prendiville, Sean.

In: arXiv, 23.03.2020.

Research output: Contribution to journalJournal articlepeer-review

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@article{4ff6b35d3fe645b9b3fbc40dcc1ad67c,
title = "Counting monochromatic solutions to diagonal Diophantine equations",
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. ",
keywords = "math.NT, math.CO",
author = "Sean Prendiville",
year = "2020",
month = mar,
day = "23",
language = "English",
journal = "arXiv",
issn = "2331-8422",

}

RIS

TY - JOUR

T1 - Counting monochromatic solutions to diagonal Diophantine equations

AU - Prendiville, Sean

PY - 2020/3/23

Y1 - 2020/3/23

N2 - 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.

AB - 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.

KW - math.NT

KW - math.CO

M3 - Journal article

JO - arXiv

JF - arXiv

SN - 2331-8422

ER -