44 citations · 156 across the 33 of their papers we have counts for
40 papers
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…
On the average number of zeros of random harmonic polynomials with i.i.d. coefficients: precise asymptotics
Erik Lundberg, Andrew Thomack
Addressing a problem posed by W. Li and A. Wei (2009), we investigate the average number of (complex) zeros of a random harmonic polynomial sampled from th…
Multiplane gravitational lenses with an abundance of images
Charles R. Keeton, Erik Lundberg, Sean Perry
We consider gravitational lensing of a background source by a finite system of point-masses. The problem of determining the maximum possible number of lensed images has been comple…
On the valence of logharmonic polynomials
Dmitry Khavinson, Erik Lundberg, Sean Perry
Investigating a problem posed by W. Hengartner (2000), we study the maximal valence (number of preimages of a prescribed point in the complex plane) of logharmonic polynomials, i.e…
Inradius of random lemniscates
Manjunath Krishnapur, Erik Lundberg, Koushik Ramachandran
A classically studied geometric property associated to a complex polynomial is the inradius (the radius of the largest inscribed disk) of its (filled) lemniscate $Λ:= \{z \in \…
The valence of harmonic polynomials viewed through the probabilistic lens
Erik Lundberg
We prove the existence of complex polynomials of degree and of degree such that the harmonic polynomial has at least $\lceil n \sq…