Ullemar's formula for the Jacobian of the complex moment mapping
Complex Variables
2009-03-02 v1 Commutative Algebra
Abstract
The complex moment sequence m(P) is assigned to a univalent polynomial P by the Cauchy transform of the P(D), where D is the unit disk. We establish the representation of the Jacobian det dm(P) in terms of roots of the derivative P'. Combining this result with the special decomposition for the Hurwitz determinants, we prove a formula for the Jacobian which was previously conjectured by C. Ullemar. As a consequence, we show that the boundary of the class of all locally univalent polynomials in is contained in the union of three irreducible algebraic surfaces.
Keywords
Cite
@article{arxiv.math/0306324,
title = {Ullemar's formula for the Jacobian of the complex moment mapping},
author = {Olga S. Kuznetsova and Vladimir G. Tkachev},
journal= {arXiv preprint arXiv:math/0306324},
year = {2009}
}
Comments
14 pages, submitted for "Complex Variables. Theory and Application"