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.
M´ erai, On divisors of sums of polynomials
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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.