On The Solvability of Bilinear Equations in Finite Fields
| dc.creator | Shparlinski, Igor E. | |
| dc.date | 2007-08-16 | |
| dc.date | 2007-09-16 | |
| dc.date.accessioned | 2026-07-07T08:29:31Z | |
| dc.date.available | 2026-07-07T08:29:31Z | |
| dc.description | We consider the equation $$ ab + cd = λ, \qquad a\in A, b \in B, c\in C, d \in D, $$ over a finite field $F_q$ of $q$ elements, with variables from arbitrary sets $ A, B, C, D \subseteq F_q$. The question of solvability of such and more general equations has recently been considered by D. Hart and A. Iosevich, who, in particular, proved that if $$ #A #B #C #D \gg q^3, $$ then above equation has a solution for any $λ\in F_q^*$. Here we show that using bounds of multiplicative character sums allows us to extend the class of sets which satisfy this property. | |
| dc.identifier | https://arxiv.org/abs/0708.2130 | |
| dc.identifier | http://arxiv.org/abs/0708.2130 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137961 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11L40, 11T30 | |
| dc.title | On The Solvability of Bilinear Equations in Finite Fields | |
| dc.type | text |