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A generalization of Roth's theorem in function fields
Abstract
Let 𝔽q[t] denote the polynomial ring over the finite field 𝔽q, and let formula denote the subset of 𝔽q[t] containing all polynomials of degree strictly less than N. For non-zero elements r1, …, rs of 𝔽q satisfying r1 + ⋯ + rs = 0, let formula denote the maximal cardinality of a set formula which contains no non-trivial solution of r1x1 + ⋯ + rsxs = 0 with xi ∈ A (1 ≤ i ≤ s). We prove that formula.
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Cite this version of the work
Yu-Ru Liu, Craig V. Spencer
(2009).
A generalization of Roth's theorem in function fields. UWSpace.
http://hdl.handle.net/10012/20000
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