Sums of dilates in groups of prime order

Abstract

We obtain a first non-trivial estimate for the sum of dilates problem in the case of groups of prime order, by showing that if $t$ is an integer different from $0,1$ or -1 and if $\A \subset \Zp$ is not too large (with respect to $p$), then $|\A+t\cdot \A|>(2+ \vartheta_t)|\A|-w(t)$ for some constant $w(t)$ depending only on $t$ and for some explicit real number ${\vartheta }_t>0$ (except in the case $|t|=3$). In the important case $|t|=2$, we may for instance take ${\vartheta }_2=0.08$.

Submitted in march

References in corpus (2)

• A Lower Bound for the Size of a Sum of Dilates
• On a sumset problem for integers

Cited by in corpus (7)

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• On a sumset problem for integers
• Sum of many dilates
• Sums of dilates in ordered groups
• A question of Bukh on sums of dilates
• Sums of dilates in ${\mathbb{Z}}_p$