The Erdős Theorem and the Halberstam Theorem in function fields
On sets of polynomials whose difference set contains no squares
Let be the polynomial ring over the finite field , and let be the subset of containing all polynomials of degree strictly less than N. Define D(N) to be the maximal cardinality of a set for which A-A contains no squares of polynomials. By combining the polynomial Hardy-Littlewood circle method with the density increment technology developed by Pintz, Steiger and Szemerédi, we prove that .
Roth's theorem on systems of linear forms in function fields
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