Conjectures on the distribution of roots modulo a prime of a polynomial

arXiv1905.02364MaRDI QIDQ6507467

Author name not available (Why is that?)

Abstract: For a given monic integral polynomial $f(x)$ of degree $n$, we define local roots $r_i$ of $f(x)$ for a completely decomposable prime $p$ by $r_{i}inmathbbZ$, $$ and $0le{r}_{1}le{r}_{2}ledotsle{r}_n<p$. With numerical data, we propose a conjecture on the distribution of $(r_1/p,dots,r_n/p)$, which is a new kind of equi-distribution, and a conjecture of the distribution of $(r_1,dots,r_n)$ which satisfies $$ for given natural numbers $L,R_1,dots,R_n$, which is nothing but Dirichlet's theorem on an arithmetic progression in the case $n=1$.

This page was built for publication: Conjectures on the distribution of roots modulo a prime of a polynomial

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6507467)