How Constant Shifts Affect the Zeros of Certain Rational Harmonic Functions

摘要

We study the effect of constant shifts on the zeros of rational harmonic functions . In particular, we characterize how shifting through the caustics of f changes the number of zeros and their respective orientations. This also yields insight into the nature of the singular zeros of f. Our results have applications in gravitational lensing theory, where certain such functions f represent gravitational point-mass lenses, and a constant shift can be interpreted as the position of the light source of the lens.