Lang's Conjecture and Sharp Height Estimates for the elliptic curves y2=x3+axy^{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.Comment: published version. Lemmas 5.1 and 6.1 now precise (with resultant refinement to Theorem 1.2). Small corrections to

Lang's conjecture and sharp height estimates for the elliptic curves y2=x3+by^{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.Comment: published version, incorporates referee's changes as well as other improvement

美作大学研究シーズ集

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小児生体肝移植後のhepatic venous outflow obstructionに対する経皮的治療の長期成績

京都大学0048新制・課程博士博士(医学)甲第18878号医博第3989号新制||医||1008(附属図書館)31829京都大学大学院医学研究科医学専攻(主査)教授 坂井 義治, 教授 坂田 隆造, 教授 平岡 眞寛学位規則第4条第1項該当Doctor of Medical ScienceKyoto UniversityDFA

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.Comment: version accepted for publication. Difference of heights result moved to http://arxiv.org/abs/1104.4645 and improved. Proof simplified to remove need for special cases when n>2