Exponential sums with reducible polynomials

Abstract

International audienceHooley proved that if f ∈ Z[X] is irreducible of degree ≥ 2, then the fractions {r/n}, 0 < r < n with f (r) ≡ 0 (mod n), are uniformly distributed in ]0, 1[. In this paper we study such problems for reducible polynomials of degree 2 and 3 and for finite products of linear factors. In particular, we establish asymptotic formulas for exponential sums over these normalized roots

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