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The Erdős Theorem and the Halberstam Theorem in function fields

100%

Liu Y.-R.

Acta Arithmetica

2004

tom 114

nr 4

323-330

On sets of polynomials whose difference set contains no squares

63%

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 $D(N) ≪ q^N( log N)^{7}/N$.

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

51%

Liu Y.-R., Spencer C., Zhao X.

Acta Arithmetica

2010

tom 142

nr 4

377-386

Ograniczanie wyników

3 Acta Arithmetica

3 Liu Y.-R.

1 Lê T.

1 Spencer C.

1 Zhao X.

1 2013

1 2010

1 2004

Wyniki wyszukiwania

The Erdős Theorem and the Halberstam Theorem in function fields

On sets of polynomials whose difference set contains no squares

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