On sets of polynomials whose difference set contains no squares

• Autorzy: Thái Hoàng Lê , Yu-Ru Liu
• Języki publikacji: EN

Abstrakty

EN

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 $D(N) ≪ q^N( log N)^{7}/N$.

Kategorie tematyczne

• 11T55: Arithmetic theory of polynomial rings over finite fields
• 11P55: Applications of the Hardy-Littlewood method

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 161
• Numer: 2
• Strony: 127-143

Daty

wydano

2013

Twórcy

autor

Thái Hoàng Lê

• Department of Mathematics, The University of Texas at Austin, 1 University Station, C1200, Austin, TX 78712, U.S.A.

autor

Yu-Ru Liu

• Department of Pure Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, ON, Canada N2L 3G1

Identyfikatory

DOI

10.4064/aa161-2-2