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This paper is a sequel to [7]. Here we study identities for the Fourier transform of "elementary functions" over finite fields containing "exponentials" of rational monomial functions. It turns out that these identities are governed by monomial identities between Gauss sums. We show that similar to the case of complex numbers such identities correspond to linear relations between certain divisors on the space of multiplicative characters.

Fourier transform over finite field and identities between Gauss sums