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A point-sphere incidence bound in odd dimensions and applications
In this paper, we prove a new point-sphere incidence bound in vector spaces over finite fields. More precisely, let be a set of points and be a set of spheres in . Suppose that , we prove that the number of incidences between and satisfies
under some conditions on , and radii. This improves the known upper bound in the literature. As an application, we show that for with , one has
This improves earlier results on this sum-product type problem over arbitrary finite fields
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