Translation invariant equations and the method of Sanders

Abstract

We extend the recent improvement of Roth's theorem on three term arithmetic progressions by Sanders to obtain similar results for the problem of locating non-trivial solutions to translation invariant linear equations in many variables in both $\bbz/N\bbz$ and $\bbf_q[t]$.

References in corpus (1)

• Roth's theorem in many variables

Cited by in corpus (6)

• A quantitative improvement for Roth's theorem on arithmetic progressions
• Four variants of the Fourier-analytic transference principle
• Maximal subsets free of arithmetic progressions in arbitrary sets
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• Some properties of lower level-sets of convolutions