On multivariable cumulant polynomial sequences with applications

Multivariable polynomial injections on rational numbers

For each number field k, the Bombieri-Lang conjecture for k-rational points on surfaces of general type implies the existence of a polynomial f(x, y) ∈ k[x, y] inducing an injection k × k → k.

Multivariable Twisted Alexander Polynomial for Hyperbolic Three–manifolds with Boundary

We consider a sign–determined Reidemeister torsion with multivariables for a hyperbolic three–dimensional manifold with cusps. Using a cut and paste argument, we prove that this Reidemeister torsion is a polynomial invariant when provided with appropriate conditions on the topology of the manifold and SL2(C)representations of its fundamental group. Under such assumptions, it is proved that this...

Rainbow, a New Multivariable Polynomial Signature Scheme

Balanced Oil and Vinegar signature schemes and the unbalanced Oil and Vinegar signature schemes are public key signature schemes based on multivariable polynomials. In this paper, we suggest a new signature scheme, which is a generalization of the Oil-Vinegar construction to improve the efficiency of the unbalanced Oil and Vinegar signature scheme. The basic idea can be described as a construct...

Eigenvalue Decomposition of a Cumulant Tensor with Applications

Multivariable Calculus, Applications and Theory