ScholarLens Back to search
2009•arXiv (Cornell University)Open access

Lang's Height Conjecture and Szpiro's Conjecture

Joseph H. Silverman

Open full text 1 citations

Abstract

It is known that Szpiro's conjecture, or equivalently the ABC-conjecture, implies Lang's conjecture giving a uniform lower bound for the canonical height of nontorsion points on elliptic curves. In this note we show that a significantly weaker version of Szpiro's conjecture, which we call "prime-depleted," suffices to prove Lang's conjecture.

Open-access reader

About this research paper

What this paper is about

It is known that Szpiro's conjecture, or equivalently the ABC-conjecture, implies Lang's conjecture giving a uniform lower bound for the canonical height of nontorsion points on elliptic curves. In this note we show that a significantly weaker version of Szpiro's conjecture, which we call "prime-depleted," suffices to prove Lang's conjecture.

Why it matters

OpenAlex reports 1 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

It is known that Szpiro's conjecture, or equivalently the ABC-conjecture, implies Lang's conjecture giving a uniform lower bound for the canonical height of nontorsion points on elliptic curves. In this note we show that a significantly weaker version of Szpiro's conjecture, which we call "prime-depleted," suffices to prove Lang's conjecture.

Key concepts: Conjecture, abc conjecture, Collatz conjecture, Elliott–Halberstam conjecture, Lonely runner conjecture, Mathematics, Combinatorics, Prime (order theory)

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Lang's Height Conjecture and Szpiro's Conjecture — Research Paper | ScholarLens