Hankel Determinant Solution for Elliptic Sequence

TL;DR

This paper demonstrates that Hankel determinants of a generalized Catalan sequence satisfy elliptic sequence equations, enabling the expression of elliptic curve point multiples through these determinants.

Contribution

It establishes a novel connection between Hankel determinants of Catalan sequences and elliptic sequences, providing explicit formulas for elliptic curve point multiples.

Findings

Hankel determinants satisfy elliptic sequence equations

Coordinates of elliptic curve multiples are expressed via Hankel determinants

Provides a new algebraic tool for elliptic curve analysis

Abstract

We show that the Hankel determinants of a generalized Catalan sequence satisfy the equations of the elliptic sequence. As a consequence, the coordinates of the multiples of an arbitrary point on the elliptic curve are expressed by the Hankel determinants.