2025/08/13 by Lazebnik, Kirill, Lundberg, Erik
#30C55 #37F10 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2508.10151
Consider a logharmonic polynomial; that is, a product of the form p(z)q(z), where p, q are holomorphic polynomials. Assume q is linear and denote by n the degree of p. It was recently shown in arXiv:2302.04339 [math.CV] that the valence of such a logharmonic polynomial is at most 3n-1; in this paper we show that their 3n-1 upper bound is sharp. Together with the work of arXiv:2302.04339 [math.CV], this resolves a conjecture of Bshouty and Hengartner.