Abstract
The known theorem of gravitational lensing that describes the relationship between the numbers of images with different parities is valid in the case in which the density profile of the lensing object is smooth. In this paper, using the complex representation of the lens equation, we reformulate the known theorem. Our formulation not only gives the known theorem for the smooth mass density profile but also gives new results for singular mass densities such as point masses model and the multipole expansion model. In order to see how the theorem works in a real event, we give the numerical fittings of quadruple images of PG 1115+080 by the regular elliptical density model and by the singular multipole expansion model.
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