Koushik Ramachandran

collaborators

4 papers

math.AP2026

Counterexamples to Magnanini's conjecture concerning critical points of the torsion function

Parker Edwards, Erik Lundberg, Koushik Ramachandran

We construct planar simply-connected domains whose torsion function has an arbitrary prescribed number of local maxima while the distance to the boundary has only one local maximum…

math.PR2026

Asymptotics of the Number of Components of Random Polynomial Lemniscates

Subhajit Ghosh, Koushik Ramachandran, Atul Shekhar

Consider a sequence of random polynomials $P_{n} (z) = \prod_{k = 1}^{n} (z - X_{k})$ , where ${X_{k}}_{k}$ are i.i.d. random variables distributed uniformly on the unit disc $D$ . Le…

math.CV2026

A note on the ErdÃ¶s minimal area problem

Subhajit Ghosh, Koushik Ramachandran

We answer a question of ErdÃ¶s, Herzog, and Piranian on the minimal area of polynomial lemniscates when all the zeros of the polynomial are constrained to lie on a compact set K wh…

math.CV2025

On the area of polynomial lemniscates

Manjunath Krishnapur, Erik Lundberg, Koushik Ramachandran

ErdÃ¶s 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…