Koushik Ramachandran

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20232026

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math.CV2026

A note on the Erdös minimal area problem

Subhajit Ghosh, Koushik Ramachandran

We answer a question of Erdős, Herzog, and Piranian \cite[Problem $4$ , page $135$ ]{EHP} on the minimal area of polynomial lemniscates when all the zeros of the polynomial are const…

math.CV2025

On the area of polynomial lemniscates

Manjunath Krishnapur, Erik Lundberg, Koushik Ramachandran

Erdös posed in 1940 the extremal problem of studying the minimal area of the lemniscate ${∣ p (z) ∣ < 1}$ of a monic polynomial $p$ of degree $n$ all of whose zeros are in the closed…

math.CV2023

Number of components of polynomial lemniscates: a problem of Erdös, Herzog, and Piranian

Subhajit Ghosh, Koushik Ramachandran

Let $K \subset C$ be a compact set in the plane whose logarithmic capacity $c (K)$ is strictly positive. Let $P_{n} (K)$ be the space of monic polynomials of degree $n…