Prendiville, Sean (2020) Counting monochromatic solutions to diagonal Diophantine equations. arXiv.
Text (2003.10161v1)
2003.10161v1.pdf - Accepted Version
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2003.10161v1.pdf - Accepted Version
Available under License Creative Commons Attribution.
Download (497kB)
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.
Item Type:
Journal Article
Journal or Publication Title:
arXiv
Subjects:
?? math.ntmath.co ??
Departments:
ID Code:
144682
Deposited By:
Deposited On:
15 Jun 2020 13:30
Refereed?:
Yes
Published?:
Published
Last Modified:
02 Oct 2024 00:20