Y. Kitaoka

activity

20172019

most citedStatistical distribution of roots of a polynomial modulo primes

1 citations · 1 across the 2 of their papers we have counts for

collaborators

4 papers

math.NT2019

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

Yoshiyuki Kitaoka

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 $r_{i} \in Z$ , $f(r_i) \equiv 0…

math.NT2018

Linear relations among roots of a polynomial

Yoshiyuki Kitaoka

Let $f (x)$ be a monic polynomial over $Q$ with complex roots $α_{1}, \dots, α_{n}$ . Linear relations among them and $1$ over $Q$ play an important role when we study th…

math.NT2017★ 1 cited

Statistical distribution of roots of a polynomial modulo primes

Yoshiyuki Kitaoka

Let $f (x) = x^{n} + a_{n - 1} x^{n - 1} + \dots + a_{0}$ be an irreducible polynomial with integer coefficients. For a prime $p$ for which $f (x)$ is fully splitting modulo $p$ , we consider $n$ roo…

math.NT2017

Behaviour of the least root modulo a prime of a polynomial

Yoshiyuki Kitaoka

For a polynomial $f (x) \in Z [x]$ without non-trivial linear relations among roots, we propose a conjecture on the distribution of the least root $r_{p}$ ($r_p\in\mathbb Z,\,0\l…