Exponential sums with reducible polynomials

Cécile Dartyge (1) , Greg Martin (2)

1 IECL - Institut Élie Cartan de Lorraine
2 UBC - University of British Columbia

Hooley 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.

Domaines: Théorie des nombres [math.NT]

Cécile Dartyge, Greg Martin. Exponential sums with reducible polynomials. Discrete Analysis, 2019, 15, 31 p. ⟨10.19086/da.10793⟩. ⟨hal-02311450⟩