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Article Dans Une Revue European Journal of Combinatorics Année : 2013

Conditional expanding bounds for two-variables functions over prime fields

Résumé

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 $\Delta(\alpha)>0$ such that if $|A|\asymp p^{\alpha}$ then $$ \max(|A+A|,|A\cdot A|)\gg |A|^{1+\Delta(\alpha)}, $$ Our aim is to obtain analogous results for related pairs of two-variable functions $f(x,y)$ and $g(x,y)$: if $|A|\asymp|B|\asymp p^{\alpha}$ then $$ \max(|f(A,B)|,|g(A,B)|)\gg |A|^{1+\Delta(\alpha)} $$ for some $\Delta(\alpha)>0$.

Dates et versions

hal-00868110 , version 1 (01-10-2013)

Identifiants

Citer

Norbert Hegyvári, François Hennecart. Conditional expanding bounds for two-variables functions over prime fields. European Journal of Combinatorics, 2013, 34, pp.1365-1382. ⟨hal-00868110⟩
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