Integer and Rational Solutions to Polynomial Equations

Abstract

A formalism is given to count integer and rational solutions to polynomial equations with rational coefficients. These polynomials $P(x)$ are parameterized by three integers, labeling an elliptic curve. The counting of the rational solutions to $y^2=P(x)$ is facilitated by another elliptic curve with integral coefficients. The problem of counting is described by two elliptic curves and a map between them.

7 pages, LaTeX

References in corpus (4)

• Geometric Solutions to Algebraic Equations
• A New Knot Invariant
• Geometric Solutions to Non-linear Differential Equations
• Knots and Polytopes

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