On sets of polynomials whose difference set contains no squares

Thái Hoàng Lê; Yu-Ru Liu

Acta Arithmetica, Tome 161 (2013), p. 127-143 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $A \subseteq_{N}$ 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 $D (N) ≪ q^{N} {(l o g N)}^{7} / N$ .

Publié le : 2013-01-01

Zbl 1294.11177

EUDML-ID : urn:eudml:doc:279659

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     title = {On sets of polynomials whose difference set contains no squares},
     journal = {Acta Arithmetica},
     volume = {161},
     year = {2013},
     pages = {127-143},
     zbl = {1294.11177},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa161-2-2}
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Thái Hoàng Lê; Yu-Ru Liu. On sets of polynomials whose difference set contains no squares. Acta Arithmetica, Tome 161 (2013) pp. 127-143. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa161-2-2/