Geodesic
ON THE SOLVABILITY OF BILINEAR EQUATIONS IN FINITE FIELDS
Glasgow mathematical journal, Tome 50 (2008) no. 3, pp. 523-529

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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.
DOI : 10.1017/S0017089508004382
Mots-clés : 11L40, 11T30 
SHPARLINSKI, IGOR E. ON THE SOLVABILITY OF BILINEAR EQUATIONS IN FINITE FIELDS. Glasgow mathematical journal, Tome 50 (2008) no. 3, pp. 523-529. doi: 10.1017/S0017089508004382
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     title = {ON {THE} {SOLVABILITY} {OF} {BILINEAR} {EQUATIONS} {IN} {FINITE} {FIELDS}},
     journal = {Glasgow mathematical journal},
     pages = {523--529},
     year = {2008},
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     number = {3},
     doi = {10.1017/S0017089508004382},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004382/}
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