V. Kostov

collaborators

6 papers

math.CA2026

Where not to find the spectrum of the partial theta function

Yousra Gati, Vladimir Petrov Kostov

The spectrum of Ramanujan's partial theta function $I^¸ (q, x) := \sum_{j = 0}^{\infty} q^{j (j + 1) /2} x^{j}$ , $q \in D_{1}$ (the unit disk centered at the origin), $x \in C$ , is…

math.CA2026

Some analytic properties of the partial theta function

Vladimir Petrov Kostov

We prove new properties of the zero set of Ramanujan's partial theta function $I^¸ (q, x) := \sum_{j = 0}^{\infty} q^{j (j + 1) /2} x^{j}$ , $q \in (- 1, 0) \cup (0, 1)$ , $x \in R$ . We show th…

math.CA2026

Three realization problems about univariate polynomials

Vladimir Petrov Kostov

We consider three realization problems about monic real univariate polynomials without vanishing coefficients. Such a polynomial $P := \sum_{j = 0}^{d} b_{j} x^{j}$ defines the sign pattern $Ï…

math.CA2025

Midpoints and critical points

Yousra Gati, Vladimir Petrov Kostov

For a degree $5$ real polynomial with roots $x_{1} \leq \dots \leq x_{5}$ and roots $I^¾_{1} \leq \dots \leq I^¾_{4}$ of its derivative, we set $z_{j} := (x_{j} + x_{j + 1}) /2$ , $1 \leq j \leq 4$ . We pr…

math.NA2025

Numerical approach for solving problems arising from polynomial analysis

Yousra Gati, Vladimir Petrov Kostov, Mohamed Chaouki Tarchi

This paper deals with the use of numerical methods based on random root sampling techniques to solve some theoretical problems arising in the analysis of polynomials. These methods…

math.CA2025

On the location of the complex conjugate zeros of the partial theta function

Vladimir Petrov Kostov

We prove that for any $q \in (0, 1)$ , all complex conjugate pairs of zeros of the partial theta function $I^¸ (q, x) := \sum_{j = 0}^{\infty} q^{j (j + 1) /2} x^{j}$ with non-negative real part be…