- 2003.10161v1
Accepted author manuscript, 486 KB, PDF document

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

- https://arxiv.org/abs/2003.10161
Final published version

Licence: CC BY: Creative Commons Attribution 4.0 International License

Research output: Contribution to journal › Journal article › peer-review

Published

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

Research output: Contribution to journal › Journal article › peer-review

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

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

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

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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. ",

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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.

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