Boris Shapiro

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math.CA2026

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 $f$ , its irreducible equation $P (z, w) = 0$ , and a compact co…

math.CA2026

Weak and strong $q$ -analogs of the Laguerre--PÃ³lya class

D. K. Dimitrov, B. Shapiro

For $0 < q < 1$ we compare two natural $q$ -analogs of the Laguerre--PÃ³lya class. The first one is a coefficient-side class, defined as the inverse image of the classical Laguerre--PÃ³…

math.CA2026

Complex spectrum of the partial theta function

Boris Shapiro

We study the complex spectrum of the partial theta function \[ Î(q,x)=\sum_{j=0}^{\infty}q^{j(j+1)/2}x^j, \qquad |q|<1, \] where a spectral value is a parameter for which \(Î(q,\…

math.CA2026

Discriminants of derivatives and symmetric difference polynomials

Boris Shapiro

Let $P$ be a monic polynomial of degree $n$ with roots $x_{1}, \dots, x_{n}$ . We study the discriminants of the derivatives $P^{(k)}$ as symmetric translation-invariant polynomials in t…

math.CA2026

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 $d$ -polytope. Such pushforwards are…

Algebraic defect and positive mother body measures

Weak and strong q-analogs of the Laguerre--PÃ³lya class

Complex spectrum of the partial theta function

Discriminants of derivatives and symmetric difference polynomials

Projections of convex polytopes to a line and higher univariate Prony systems

Weak and strong $q$ -analogs of the Laguerre--PÃ³lya class