Teng Zhang

activity

20242026

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4 papers · 1 filter

math.CV2026

Proof of the Agler--McCarthy entropy conjecture

Jialin Lei, Teng Zhang

In 2021, J.~Agler and J.~E. McCarthy proposed a two-step programme toward the celebrated KrzyÅ¼ conjecture. The first step is to prove an entropy conjecture for polynomials whose z…

math.CV2026

Intersections of Convex Hulls of Polynomial Shifts and Critical Points

Teng Zhang

Let $p (z)$ be a complex polynomial of degree $n \geq 2$ . For each $c \in C$ , let $K_{c}$ denote the convex hull of the zeros of $p (z) + c$ , and let $K^{'}$ denote the convex hull of…

math.CV2026

Angle duality and a gap principle for convex combinations of incomplete polynomials on the unit circle

Teng Zhang

In this paper, we establish an angle duality and a gap principle for convex combinations of incomplete polynomials, extending two results of Ge and Gonek in [IMRN, 2024].Our approa…

math.CV2025

Sharp Schoenberg type inequalities and the de Bruin--Sharma problem

Quanyu Tang, Teng Zhang

In this paper, we confirm two conjectures proposed by Georgiev, GÃ³mez-Serrano, Tao, and Wagner~\cite{GGTW25} on Schoenberg type inequalities of order $4$ , thereby providing a comp…