Autor:	Prendiville, Sean
Rok vydání:	2020
Předmět:	Mathematics - Number Theory Mathematics - Combinatorics
Druh dokumentu:	Working Paper
Popis:	We show how to adapt the Hardy--Littlewood circle method to count monochromatic solutions to diagonal Diophantine equations. This delivers a lower bound which is optimal up to absolute constants. The method is illustrated on equations obtained 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. Comment: v2. Incorporates referees' suggestions and Discrete Analysis style file
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2003.10161 Zobrazit plný text záznamu View this record from Arxiv