Estimates for the count of m-smooth polynomials in F_q[t] with several prescribed coefficients are obtained via character sum estimates, Bourgain's argument adapted to polynomials, and double character sums.
Gorodetsky, Mean values of arithmetic functions in short int ervals and in arithmetic progressions in the large-degree limit, Mathematika 66 (2020), no
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Smooth polynomials with several prescribed coefficients
Estimates for the count of m-smooth polynomials in F_q[t] with several prescribed coefficients are obtained via character sum estimates, Bourgain's argument adapted to polynomials, and double character sums.