Proof of Serge Lang's Heights Conjecture and an almost optimal Bound for the Torsion of Elliptic Curves

2017/01/25 by Benjamin Wagener, Wagener, Benjamin
Computer Science · Mathematics · #11G50 11D75 11D99 11G05 11G07 11G99 11H99 11J25 11J68 11J81 11J82 11J86 11J99 14G05 14G22 14G25 14G40 14G99 14H52 14H99 14J20 14K15 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1701.07433

openalex publication_date 2017/01/25 · openalex created_date 2017/02/10 · openalex updated_date 2026/07/28

Abstract

This paper focuses on the proof of Serge Lang's Heights Conjecture in a form that is completely effective. As a complementary result the author provides a new proof of Mazur-Merel theorem about a bound for the torsion of elliptic curves in terms of the degree of the ground field and improves the known result by providing a small polynomial bound in terms of this degree. (Submitted)

Related

• About the Proof of Lang's Height Conjecture
• Explicit height bounds and the explicit Mordell-Lang Conjecture
• Experimental investigations on Lehmer's conjecture for elliptic curves
• A statistical view on the conjecture of Lang about the canonical height on elliptic curves
• Heights of points on elliptic curves over \mathbb Q