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ON THE SOLVABILITY OF BILINEAR EQUATIONS IN FINITE FIELDS

Published online by Cambridge University Press:  01 September 2008

IGOR E. SHPARLINSKI
IGOR E. SHPARLINSKI*
Affiliation:
Department of Computing, Macquarie University, Sydney, NSW 2109, Australia e-mail: [email protected]
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Abstract

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We consider the equation over 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 if for 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.

Keywords

11L4011T30
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 3 , September 2008 , pp. 523 - 529
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

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