An improved bound on the sum-product estimate in $\mathbb{F}_{p}$

Abstract: We give an improved bound on the famed sum-product estimate in a field of residue class modulo $p$ ($\mathbb{F}{p}$) by Erd\H{o}s and Szemeredi, and a non-empty set $A \subset \mathbb{F}{p}$ such that: $$ \max {|A+A|,|A A|} \gg \min \left{\frac{|A|^{15 / 14} \max \left{1,|A|^{1 / 7} p^{-1 / 14}\right}}{(\log |A|)^{2 / 7}}, \frac{|A|^{11 / 12} p^{1 / 12}}{(\log |A|)^{1 / 3}}\right}, $$ and more importantly: $$\max {|A+A|,|A A|} \gg \frac{|A|^{15 / 14}}{(\log |A|)^{2 / 7}}.$$