On the sum of dilations of a set

Antal Balog; George Shakan

Acta Arithmetica, Tome 166 (2014), p. 153-162 / Harvested from The Polish Digital Mathematics Library

Résumé

We show that for any relatively prime integers 1 ≤ p < q and for any finite A ⊂ ℤ one has ${| p \cdot A + q \cdot A | \geq (p + q) | A | - (p q)}^{(p + q - 3) (p + q) + 1}$ .

Publié le : 2014-01-01

Zbl 06307061

EUDML-ID : urn:eudml:doc:279398

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     author = {Antal Balog and George Shakan},
     title = {On the sum of dilations of a set},
     journal = {Acta Arithmetica},
     volume = {166},
     year = {2014},
     pages = {153-162},
     zbl = {06307061},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-2-5}
}

Antal Balog; George Shakan. On the sum of dilations of a set. Acta Arithmetica, Tome 166 (2014) pp. 153-162. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-2-5/