Liu, Yu-RuSpencer, Craig V.2023-10-032023-10-032009-11https://doi.org/10.1142/S1793042109002602http://hdl.handle.net/10012/20000Electronic version of an article published as LIU, Y.-R., & SPENCER, C. V. (2009). A generalization of Roth’s theorem in function fields. International Journal of Number Theory, 05(07), 1149–1154. https://doi.org/10.1142/s1793042109002602 © 2009. World Scientific Publishing Company. https://www.worldscientific.com/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.enArticle