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Resumen de Bilinear character sums over norm groups

Su Hu, Yan Li

  • Let k be a nite eld with q elements. Let kn be the extension of k with degree n.

    Let Nn be the kernel of the norm map Nkn=k : k n ! k. In this paper we estimate the bilinear character sum W;( ;U; V) = Ó U2U Ó V 2V (U)(V ) (UV );

    where U and V are arbitrary subsets of Nn, (U) and (V ) are arbitrary bounded complex functions supported on U and V and is a nontrivial additive character of kn. We apply this bound to two problems.

    (1) If S, T, U, V are subsets of Nn, we study the equation S +T = UV , where S 2 S, T 2 T, U 2 U, V 2 V.

    (2) We study the Nn analogy of the sum-product problem

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