ON THE SOLVABILITY OF BILINEAR EQUATIONS IN FINITE FIELDS

SHPARLINSKI, IGOR E.

Glasgow mathematical journal, Tome 50 (2008) no. 3, pp. 523-529

Résumé

We consider the equationover a finite field q of q elements, with variables from arbitrary sets. The question of solvability of such and more general equations has recently been considered by Hart and Iosevich, who, in particular, prove that iffor some absolute constant C > 0, then above equation has a solution for any λ ∈ q*. Here we show that using bounds of multiplicative character sums allows us to extend the class of sets which satisfy this property.

Détail

DOI : 10.1017/S0017089508004382

Mots-clés : 11L40, 11T30

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