4 papers · 1 filter
Algebraic defect and positive mother body measures
Boris Shapiro
Continuing the study of mother-body measures with algebraic Cauchy transform, we associate with a positive algebraic germ , its irreducible equation , and a compact co…
Complex spectrum of the partial theta function
Boris Shapiro
We study the complex spectrum of the partial theta function \[ Θ(q,x)=\sum_{j=0}^{\infty}q^{j(j+1)/2}x^j, \qquad |q|<1, \] where a spectral value is a parameter for which \(Θ(q,\cd…
Projections of convex polytopes to a line and higher univariate Prony systems
Boris Shapiro
Motivated by the inverse moment problem for convex polytopes, we study the pushforward to a line of the Lebesgue measure restricted to a convex -polytope. Such pushforwards are…
Discriminants of derivatives: square graphs and sums of squares
Boris Shapiro, Cordian Riener
The discriminants of the derivatives of a real-rooted polynomial are nonnegative polynomials in its roots, and we ask whether this nonnegativity can be certified algebraically in t…