English

Exponential sums with reducible polynomials

Number Theory 2019-11-14 v2

Abstract

Hooley proved that if fZ[X]f\in \Bbb Z [X] is irreducible of degree 2\ge 2, then the fractions {r/n}\{ r/n\}, 0<r<n0<r<n with f(r)0(modn)f(r)\equiv 0\pmod n, are uniformly distributed in (0,1)(0,1). In this paper we study such problems for reducible polynomials of degree 22 and 33 and for finite products of linear factors. In particular, we establish asymptotic formulas for exponential sums over these normalized roots.

Keywords

Cite

@article{arxiv.1802.09090,
  title  = {Exponential sums with reducible polynomials},
  author = {Cécile Dartyge and Greg Martin},
  journal= {arXiv preprint arXiv:1802.09090},
  year   = {2019}
}

Comments

31 pages

R2 v1 2026-06-23T00:32:55.371Z