Conditional expanding bounds for two-variables functions over prime fields

In this paper we provide in $\bFp$ expanding lower bounds for two variables functions $f(x,y)$ in connection with the product set or the sumset. The sum-product problem has been hugely studied in the recent past. A typical result in $\bFp^*$ is the existenceness of $Δ(α)>0$ such that if $|A|\asymp p^α$ then $\max(|A+A|,|A\cdot A|)\gg |A|^{1+Δ(α)},$ Our aim is to obtain analogous results for related pairs of two-variable functions $f(x,y)$ and $g(x,y)$: if $|A|\asymp|B|\asymp p^α$ then $\max(|f(A,B)|,|g(A,B)|)\gg |A|^{1+Δ(α)}$ for some $Δ(α)>0$.

No reviews yet.

No comments yet.