Reverse asymptotic estimates for roots of the cuboid characteristic equation in the case of the second cuboid conjecture
arXiv:1505.00724
Abstract
A perfect cuboid is a rectangular parallelepiped whose edges, whose face diagonals, and whose space diagonal are of integer lengths. The second cuboid conjecture specifies a subclass of perfect cuboids described by one Diophantine equation of tenth degree and claims their non-existence within this subclass. This Diophantine equation has two parameters. Previously asymptotic expansions and estimates for roots of this equation were obtained in the case where the first parameter is fixed and the other tends to infinity. In the present paper reverse asymptotic expansions and estimates are derived in the case where the second parameter is fixed and the first one tends to infinity. Their application to the perfect cuboid problem is discussed.
AmSTeX, 17 pages, amsppt style. arXiv admin note: substantial text overlap with arXiv:1504.07161
References in corpus (14)
- A note on the third cuboid conjecture. Part I
- Perfect cuboids and multisymmetric polynomials
- On an ideal of multisymmetric polynomials associated with perfect cuboids
- On the equivalence of cuboid equations and their factor equations
- A biquadratic Diophantine equation associated with perfect cuboids
- A general rational solution of an equation associated with perfect cuboids
- Inverse problems associated with perfect cuboids
- On singularities of the inverse problems associated with perfect cuboids
- On two algebraic parametrizations for rational solutions of the cuboid equations
- A note on rational and elliptic curves associated with the cuboid factor equations
- A note on solutions of the cuboid factor equations
- On two elliptic curves associated with perfect cuboids
- Parametric Solutions for a Nearly-Perfect Cuboid
- Two and three descent for elliptic curves associated with perfect cuboids