arXiv subjects

Minoru Yabuta

Publications and source records attributed to Minoru Yabuta.

4 recordsLinked to original sources

arXiv2021

The greatest common valuation of $ϕ_{n}$ and $ψ_{n}^{2}$ at points on elliptic curves

Given a minimal model of an elliptic curve, $E/K$, over a finite extension, $K$, of ${\mathbb Q}_{p}$ for any rational prime, $p$, and any point $P \in E(K)$ of infinite order, we determine precisely $\min \left( v \left( ϕ_{n}(P) \right), v \left( ψ_{n}^{2}(P) \right) \right)$, where $v$ is a normalised valuation on $K$ and $ϕ_{n}(P)$ and $ψ_{n}(P)$ are polynomials arising from multiplication by $n$ for this model of the curve.

math.NT↗

arXiv2016

Lang's conjecture and sharp height estimates for the elliptic curves $y^{2}=x^{3}+b$

For $E_{b}: y^{2}=x^{3}+b$, we establish Lang's conjecture on a lower bound for the canonical height of non-torsion points along with upper and lower bounds for the difference between the canonical and logarithmic height. In many cases, our results are actually best-possible.

math.NT↗

arXiv2013

Lang's Conjecture and Sharp Height Estimates for the elliptic curves $y^{2}=x^{3}+ax$

For elliptic curves given by the equation $E_{a}: y^{2}=x^{3}+ax$, we establish the best-possible version of Lang's conjecture on the lower bound of the canonical height of non-torsion points along with best-possible upper and lower bounds for the difference between the canonical and logarithmic height.

math.NT↗

arXiv2011

Primitive Divisors of Certain Elliptic Divisibility Sequences

Let $P$ be a non-torsion point on the elliptic curve $E_{a}: y^{2}=x^{3}+ax$. We show that if $a$ is fourth-power-free and either $n>2$ is even or $n>1$ is odd with $x(P)<0$ or $x(P)$ a perfect square, then the $n$-th element of the elliptic divisibility sequence generated by $P$ always has a primitive divisor.

math.NT↗