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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 Journal/Magazine › Journal article › peer-review

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Counting monochromatic solutions to diagonal Diophantine equations. / Prendiville, Sean.
In: arXiv, 23.03.2020.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Prendiville, S 2020, 'Counting monochromatic solutions to diagonal Diophantine equations', arXiv. <https://arxiv.org/abs/2003.10161>

APA

Prendiville, S. (2020). Counting monochromatic solutions to diagonal Diophantine equations. arXiv. https://arxiv.org/abs/2003.10161

Vancouver

Prendiville S. Counting monochromatic solutions to diagonal Diophantine equations. arXiv. 2020 Mar 23.

Author

Prendiville, Sean. / Counting monochromatic solutions to diagonal Diophantine equations. In: arXiv. 2020.

Bibtex

@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",

}

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

ER -