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ON A DIAGONAL QUADRIC IN DENSE VARIABLES

Published online by Cambridge University Press:  22 August 2014

EUGEN KEIL
EUGEN KEIL*
Affiliation:
Howard House, Department of Mathematics, University Walk, Clifton, Bristol BS8 1TW, United Kingdom e-mails: maxek@bristol.ac.uk Mathematical Institute, 24-29 St Giles', Oxford OX1 3LB, United Kingdom e-mails: Eugen.Keil@maths.ox.ac.uk
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Abstract

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We examine the solubility of a diagonal, translation invariant, quadratic equation system in arbitrary (dense) subsets $\mathcal{A}$ ⊂ ℤ and show quantitative bounds on the size of $\mathcal{A}$ if there are no non-trivial solutions. We use the circle method and Roth's density increment argument. Due to a restriction theory approach we can deal with equations in s ≥ 7 variables.

Keywords

Primary 11B30Secondary 11P5511D0911L07

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 3 , September 2014 , pp. 601 - 628
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

References

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