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

Derrick Hart. "A note on sumsets of subgroups in $ℤ*_{p}$." Acta Arithmetica 161.4 (2013): 387-395. <http://eudml.org/doc/279312>.

@article{DerrickHart2013,
abstract = {Let A be a multiplicative subgroup of $ℤ*_p$. Define the k-fold sumset of A to be $kA = \{x_1 + ... + x_k : x_i ∈ A, 1 ≤ i ≤ k\}$. We show that $6A ⊇ ℤ*_p$ for $|A| > p^\{11/23+ϵ\}$. In addition, we extend a result of Shkredov to show that $|2A| ≫ |A|^\{8/5-ϵ\}$ for $|A| ≪ p^\{5/9\}$.},
author = {Derrick Hart},
journal = {Acta Arithmetica},
keywords = {multiplicative subgroups; sumsets; sum-product},
language = {eng},
number = {4},
pages = {387-395},
title = {A note on sumsets of subgroups in $ℤ*_\{p\}$},
url = {http://eudml.org/doc/279312},
volume = {161},
year = {2013},
}

TY - JOUR
AU - Derrick Hart
TI - A note on sumsets of subgroups in $ℤ*_{p}$
JO - Acta Arithmetica
PY - 2013
VL - 161
IS - 4
SP - 387
EP - 395
AB - Let A be a multiplicative subgroup of $ℤ*_p$. Define the k-fold sumset of A to be $kA = {x_1 + ... + x_k : x_i ∈ A, 1 ≤ i ≤ k}$. We show that $6A ⊇ ℤ*_p$ for $|A| > p^{11/23+ϵ}$. In addition, we extend a result of Shkredov to show that $|2A| ≫ |A|^{8/5-ϵ}$ for $|A| ≪ p^{5/9}$.
LA - eng
KW - multiplicative subgroups; sumsets; sum-product
UR - http://eudml.org/doc/279312
ER -