A note on sumsets of subgroups in ${\mathbb{Z}}_p^{\ast }$

Abstract

Let $A$ be a multiplicative subgroup of ${\mathbb{Z}}_p^{\ast }$. Define the $k$-fold sumset of $A$ to be $kA=\{x_1+\cdots +x_k:x_i\in A,1\le i\le k\}$. We show that $6A\supseteq {\mathbb{Z}}_p^{\ast }$ for $|A|>p^{\frac{11}{23}+\epsilon }$. In addition, we extend a result of Shkredov to show that $|2A|\gg |A{|}^{\frac{8}{5}-\epsilon }$ for $|A|\ll p^{\frac{5}{9}}$.

References in corpus (1)

• On a question of Cochrane and Pinner concerning multiplicative subgroups

Cited by in corpus (2)

• On exponential sums over multiplicative subgroups of medium size
• On tripling constant of multiplicative subgroups