Geodesic
A note on sumsets of subgroups in ${\mathbb Z}_{p}^{*}$
Derrick Hart1
1 Department of Mathematics Rockhurst University Kansas City, MO 64110, U.S.A.
Acta Arithmetica, Tome 161 (2013) no. 4, pp. 387-395.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $A$ be a multiplicative subgroup of $\mathbb Z_p^*$. Define the $k$-fold sumset of $A$ to be $kA=\{x_1+\dots +x_k:x_i \in A$, $1\leq i\leq k\}$. We show that $6A\supseteq \mathbb Z_p^*$ for $|A| > p^{11/23 +\epsilon }$. In addition, we extend a result of Shkredov to show that $|2A|\gg |A|^{8/5-\epsilon }$ for $|A|\ll p^{5/9}$.
DOI : 10.4064/aa161-4-5
Keywords: multiplicative subgroup mathbb * define k fold sumset ka dots i leq leq supseteq mathbb * epsilon addition extend result shkredov epsilon

Derrick Hart 1

1 Department of Mathematics Rockhurst University Kansas City, MO 64110, U.S.A. 
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Derrick Hart. A note on sumsets of subgroups in ${\mathbb Z}_{p}^{*}$. Acta Arithmetica, Tome 161 (2013) no. 4, pp. 387-395. doi : 10.4064/aa161-4-5. http://geodesic.mathdoc.fr/articles/10.4064/aa161-4-5/

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