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تسجيل مستخدم جديدExtension Theorems for Spheres in the Finite Field Setting
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In this paper we study the boundedness of extension operators associated with spheres in vector spaces over finite fields.In even dimensions, we estimate the number of incidences between spheres and points in the translated set from a subset of spheres. As a result, we improve the Tomas-Stein exponents, our previous results. The analytic approach and the explicit formula for Fourier transform of the characteristic function on spheres play an important role to get good bounds for exponential sums.
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In this paper we study the $L^p-L^r$ boundedness of the extension operators associated with paraboloids in vector spaces over finite fields.In higher even dimensions, we estimate the number of additive quadruples in the subset $E$ of the paraboloids,
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The first purpose of this paper is to provide new finite field extension theorems for paraboloids and spheres. By using the unusual good Fourier transform of the zero sphere in some specific dimensions, which has been discovered recently in the work
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