The Libraries will be performing routine maintenance on UWSpace on October 20th, 2025, from 10:00-10:30 pm ET. UWSpace will be unavailable during this time. Service should resume by 10:30 pm ET.
 

On sets of polynomials whose difference set contains no squares

Loading...
Thumbnail Image

Date

2013

Authors

Hoang Le, Thai
Liu, Yu-Ru

Advisor

Journal Title

Journal ISSN

Volume Title

Publisher

Institute of Mathematics: Polish Academy of Sciences

Abstract

Let Fq[t] be the polynomial ring over the finite field Fq, and let GN be the subset of Fq[t] containing all polynomials of degree strictly less than N. Define D(N) to be the maximal cardinality of a set A⊆GN 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)≪qN(logN)7/N.

Description

Keywords

Sarkozy's theorem, function fields, circle method

LC Subject Headings

Citation