Abstract
Recently, an analogue over of Landau's theorem on sums of two squares was considered by Bary-Soroker, Smilansky and Wolf. They counted the number of monic polynomials in of degree of the form , which we denote by . They studied in two limits: fixed and large ; and fixed and large . We generalize their result to the most general limit . More precisely, we prove for an explicit constant . Our methods are different and are based on giving explicit bounds on the coefficients of generating functions. These methods also apply to other problems, related to polynomials with prime factors of even degree.
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