Abstract
Let 𝔽q be the finite field with q elements and P(x, y) be a polynomial in 𝔽q[x, y]. Using additive character sum estimates, we study expander property of the function x1 + P(x2, x3). We give an alternative proof using spectra of sum–product graphs in the case of P(x, y) = xy, and also extend the problem in the setting of finite cyclic rings.
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