Descartes' rule of signs and moduli of roots

Abstract

A hyperbolic polynomial (HP) is a real univariate polynomial with all roots real. By Descartes' rule of signs a HP with all coefficients nonvanishing has exactly $c$ positive and exactly $p$ negative roots counted with multiplicity, where $c$ and $p$ are the numbers of sign changes and sign preservations in the sequence of its coefficients. For $c=1$ and $2$, we discuss the question: When the moduli of all the roots of a HP are arranged in the increasing order on the real half-line, at which positions can be the moduli of its positive roots depending on the positions of the sign changes in the sequence of coefficients?

References in corpus (1)

• On the multivariate Fujiwara bound for exponential sums

Cited by in corpus (6)

• Hyperbolic polynomials and canonical sign patterns
• Univariate polynomials and the contractibility of certain sets
• On Descartes' rule of signs for hyperbolic polynomials
• Descartes' rule of signs, canonical sign patterns and rigid orders of moduli
• Sign patterns and rigid moduli orders
• Moduli of roots of hyperbolic polynomials and Descartes' rule of signs