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Green-Tao theorem in function fields

100%

Lê T.

Acta Arithmetica

2011

tom 147

nr 2

129-152

On sets of polynomials whose difference set contains no squares

84%

Lê T., Liu Y.-R.

Acta Arithmetica

2013

tom 161

nr 2

127-143

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

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2 Acta Arithmetica

2 Lê T.

1 Liu Y.-R.

1 2013

1 2011

Wyniki wyszukiwania

Green-Tao theorem in function fields

On sets of polynomials whose difference set contains no squares