On sets of polynomials whose difference set contains no squares

Thái Hoàng Lê, and Yu-Ru Liu. "On sets of polynomials whose difference set contains no squares." Acta Arithmetica 161.2 (2013): 127-143. <http://eudml.org/doc/279659>.

@article{TháiHoàngLê2013,
abstract = {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 $A ⊆ _\{N\}$ 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 $D(N) ≪ q^N( log N)^\{7\}/N$.},
author = {Thái Hoàng Lê, Yu-Ru Liu},
journal = {Acta Arithmetica},
keywords = {function field; circle method; difference set; finite field},
language = {eng},
number = {2},
pages = {127-143},
title = {On sets of polynomials whose difference set contains no squares},
url = {http://eudml.org/doc/279659},
volume = {161},
year = {2013},
}

TY - JOUR
AU - Thái Hoàng Lê
AU - Yu-Ru Liu
TI - On sets of polynomials whose difference set contains no squares
JO - Acta Arithmetica
PY - 2013
VL - 161
IS - 2
SP - 127
EP - 143
AB - 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 $A ⊆ _{N}$ 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 $D(N) ≪ q^N( log N)^{7}/N$.
LA - eng
KW - function field; circle method; difference set; finite field
UR - http://eudml.org/doc/279659
ER -