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Statistical distribution of roots of a polynomial modulo primes (1706.08636v1)

Published 27 Jun 2017 in math.NT

Abstract: Let $f(x)=xn+a_{n-1}x{n-1}+\dots+a_0$ be an irreducible polynomial with integer coefficients. For a prime $p$ for which $f(x)$ is fully splitting modulo $ p$, we consider $n$ roots $r_i$ of $f(x)\equiv 0\bmod p$ with $0 \le r_1\le\dots\le r_n<p$ and propose several conjectures on the distribution of an integer $\lceil \sum_{i\in S} r_i/p\rceil$ for a subset $S$ of ${1,\dots,n}$ when $p\to\infty$.

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