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arXiv · 1802.09090

Exponential sums with reducible polynomials

Cécile Dartyge·Greg Martin
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Abstract

Hooley proved that if $f\in \Bbb Z [X]$ is irreducible of degree $\ge 2$, then the fractions $\{ r/n\}$, $0<r<n$ with $f(r)\equiv 0\pmod n$, 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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Cécile Dartyge, Greg Martin. 2019-11-13. Exponential sums with reducible polynomials. https://doi.org/10.19086/da.10793

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