Abstract
AbstractWe consider the equation
over a finite field q of q elements, with variables from arbitrary sets
$\cA,\cB, \cC, \cD \subseteq \F_q$. The question of solvability of such and more general equations has recently been considered by Hart and Iosevich, who, in particular, prove that if
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.
Publisher
Cambridge University Press (CUP)
Reference21 articles.
1. Bilinear character sums over elliptic curves
2. Garaev's inequality in finite fields not of prime order;Katz;J. Anal. Combin.,2008
3. Basic Analytic Number Theory
4. The distribution of values of Dirichlet characters on additive sequences;Karatsuba;Doklady Acad. Sci. USSR,1991
Cited by
23 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献