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Currently displaying 1 – 3 of 3

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The Erdős Theorem and the Halberstam Theorem in function fields

Yu-Ru Liu — 2004

Acta Arithmetica

On sets of polynomials whose difference set contains no squares

Thái Hoàng Lê; Yu-Ru Liu — 2013

Acta Arithmetica

Let $_{q} [t]$ be the polynomial ring over the finite field $_{q}$ , and let $_{N}$ be the subset of $_{q} [t]$ containing all polynomials of degree strictly less than N. Define D(N) to be the maximal cardinality of a set $A \subseteq_{N}$ 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 $D (N) ≪ q^{N} {(l o g N)}^{7} / N$ .

Roth's theorem on systems of linear forms in function fields

Yu-Ru Liu; Craig V. Spencer; Xiaomei Zhao — 2010

Acta Arithmetica

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