On the solvability of Bilinear equations in finite fields

被引:24
|
作者
Shparlinski, Igor E. [1 ]
机构
[1] Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia
基金
澳大利亚研究理事会;
关键词
D O I
10.1017/S0017089508004382
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider the equation ab + cd = lambda, a is an element of A, b is an element of B, c is an element of C, d is an element of D, over a finite field F(q) of q elements, with variables from arbitrary sets A, B, C, D subset of F(q), The question of solvability of such and more general equations has recently been considered by Hart and Iosevich, who, in particular, prove that if #A#B#C#D >= Cq(3), for some absolute constant C > 0, then above equation has a solution for any lambda is an element of F(q)*. Here we show that using bounds of multiplicative character sums allows us to extend the class of sets which satisfy this property.
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页码:523 / 529
页数:7
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