Solution-free sets for sums of binary forms

Sean M. Prendiville

doi:10.1112/plms/pds083

Solution-free sets for sums of binary forms

Sean M. Prendiville^*

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

4 Citations (Scopus)

Abstract

In this paper, we obtain quantitative estimates for the asymptotic density of subsets of the integer lattice Z(2) that contain only trivial solutions to an additive equation involving binary forms. In the process we develop an analogue of Vinogradov's mean value theorem applicable to binary forms.

Original language	English
Pages (from-to)	267-302
Number of pages	36
Journal	Proceedings of the London Mathematical Society
Volume	107
DOIs	https://doi.org/10.1112/plms/pds083
Publication status	Published - Aug 2013

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THEOREM
EQUATIONS

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title = "Solution-free sets for sums of binary forms",

abstract = "In this paper, we obtain quantitative estimates for the asymptotic density of subsets of the integer lattice Z(2) that contain only trivial solutions to an additive equation involving binary forms. In the process we develop an analogue of Vinogradov's mean value theorem applicable to binary forms.",

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AB - In this paper, we obtain quantitative estimates for the asymptotic density of subsets of the integer lattice Z(2) that contain only trivial solutions to an additive equation involving binary forms. In the process we develop an analogue of Vinogradov's mean value theorem applicable to binary forms.

KW - THEOREM

KW - EQUATIONS

U2 - 10.1112/plms/pds083

DO - 10.1112/plms/pds083

M3 - Article (Academic Journal)

SN - 0024-6115

VL - 107

SP - 267

EP - 302

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

ER -

Solution-free sets for sums of binary forms

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