shifa liu

Rigorous Foundations for Differential Algebraic Approaches to Elliptic Curve Ranks: A Critical Reconstruction and Comprehensive Development

2025 · Zenodo (CERN European Organization for Nuclear Research)

This paper establishes a comprehensive differential algebraic framework for studying the ranks of elliptic curves, with explicit combinatorial structures and computational algorithms. We construct a rigorously defined Differential Universal Extension ME using ultraproduct techniques and …