A note on sumsets of subgroups in $ℤ*_{p}$

Derrick Hart

A note on sumsets of subgroups in

ℤ *_{p}

Derrick Hart

Acta Arithmetica, Tome 161 (2013), p. 387-395 / Harvested from The Polish Digital Mathematics Library

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Résumé

Let A be a multiplicative subgroup of $ℤ *_{p}$ . Define the k-fold sumset of A to be $k A = x_{1} + . . . + x_{k} : x_{i} \in A, 1 \leq i \leq k$ . We show that $6 A \supseteq ℤ *_{p}$ for $| A | > p^{11 / 23 + ϵ}$ . In addition, we extend a result of Shkredov to show that ${| 2 A | ≫ | A |}^{8 / 5 - ϵ}$ for $| A | ≪ p^{5 / 9}$ .

Publié le : 2013-01-01

Zbl 1286.11015

EUDML-ID : urn:eudml:doc:279312

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     title = {A note on sumsets of subgroups in $$\mathbb{Z}$*\_{p}$
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     journal = {Acta Arithmetica},
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     year = {2013},
     pages = {387-395},
     zbl = {1286.11015},
     language = {en},
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Derrick Hart. A note on sumsets of subgroups in $ℤ*_{p}$
            . Acta Arithmetica, Tome 161 (2013) pp. 387-395. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa161-4-5/