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arXiv · 1303.2729

A note on sumsets of subgroups in $\mathbb Z_p^*$

Derrick Hart
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Abstract

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 $|A| > p^{\frac {11}{23} +ε}$. In addition, we extend a result of Shkredov to show that $|2A|\gg |A|^{\frac 85-ε}$ for $|A|\ll p^{\frac 59}$.

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Derrick Hart. 2013-05-23. A note on sumsets of subgroups in $\mathbb Z_p^*$. https://arxiv.org/abs/1303.2729

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