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- W4288358664 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 $r_i in mathbb{Z}$, $f(r_i) equiv 0 bmod p$ and $0 le r_1 le r_2 le dots le r_n < p$. 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 $r_i equiv R_i bmod L$ for given natural numbers $L,R_1,dots,R_n$, which is nothing but Dirichlet's theorem on an arithmetic progression in the case $n = 1$." @default.
- W4288358664 created "2022-07-29" @default.
- W4288358664 creator A5073003552 @default.
- W4288358664 date "2019-05-07" @default.
- W4288358664 modified "2023-09-24" @default.
- W4288358664 title "Conjectures on the distribution of roots modulo a prime of a polynomial" @default.
- W4288358664 doi "https://doi.org/10.48550/arxiv.1905.02364" @default.
- W4288358664 hasPublicationYear "2019" @default.
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