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Diophantine approximation on abelian varieties; a conjecture of M. Waldschmidt

Lior Fishman,D. Lambert,Keith Merrill,David Simmons

Published 2025 in Unknown venue

ABSTRACT

Following the work of Waldschmidt, we investigate problems in Diophantine approximation on abelian varieties. First we show that a conjecture of Waldschmidt for a given simple abelian variety is equivalent to a well-known Diophantine condition holding for a certain matrix related to that variety. We then posit a related but weaker conjecture, and establish the upper bound direction of that conjecture in full generality. For rank 1 elliptic curves defined over a number field $K \subset \mathbb{R}$, we then obtain a weak-type Dirichlet theorem in this setting, establish the optimality of this statement, and prove our conjecture in this case.

PUBLICATION RECORD

  • Publication year

    2025

  • Venue

    Unknown venue

  • Publication date

    2025-06-23

  • Fields of study

    Mathematics

  • Identifiers
    arXiv 2506.19060
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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