Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them. Problems in ...

A new method for the simultaneous approximation of all the roots of a polynomial is given. The method converges for almost every initial approximation, the set of the exceptional starting points being ...

This paper concerns the location of roots of polynomials with respect to the principal coordinate axes (referred to generally as the Routh-Hurwitz criteria and the Sturm criteria). It provides a new ...