A statistical view on the conjecture of Lang about the canonical height on elliptic curves

DOI10.1090/tran/7912zbMath1473.11137arXiv1902.08435OpenAlexW2952960373WikidataQ123011867 ScholiaQ123011867MaRDI QIDQ5243106

Pierre Le Boudec

Publication date: 14 November 2019

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.08435

zbMATH Keywords

elliptic curvesrational pointscanonical height

Mathematics Subject Classification ID

Rational points (14G05) Elliptic curves over global fields (11G05) Counting solutions of Diophantine equations (11D45) Heights (11G50)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves
• Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves
• Lang's height conjecture and Szpiro's conjecture
• Lower bounds for height functions
• The canonical height and integral points on elliptic curves
• Lower bound for the canonical height on elliptic curves
• Mean values of derivatives of modular \(L\)-series
• Einige Sätze über quadratfreie Zahlen
• The average rank of elliptic curves. I. (With an appendix by Oisín McGuinness: The explicit formula for elliptic curves over function fields)
• Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0
• Height of rational points on quadratic twists of a given elliptic curve
• Inhomogeneous cubic congruences and rational points on del Pezzo surfaces
• A positive proportion of elliptic curves over $\mathbb{Q}$ have rank one
• The Difference Between the Weil Height and the Canonical Height on Elliptic Curves
• The Arithmetic of Elliptic Curves
• Heuristics on Tate-Shafarevitch Groups of Elliptic Curves Defined over Q
• Low-Lying Zeros of Maass Form L-Functions
• On the order of vanishing of modular $L$-functions at the critical point

This page was built for publication: A statistical view on the conjecture of Lang about the canonical height on elliptic curves