Abstract. The well-known Hermite-Biehler theorem claims that a univariate monic polynomial s of degree k has all roots in the open upper half-plane if and only if s = p + iq, wherepand q are real polynomials of degree k and k − 1 respectively with all real, simple and interlacing roots, and q has a negative leading coefficient. Considering roots of p as cyclically ordered on RP 1 we show that the open disk in CP 1 having a pair of consecutive roots of p as its diameter is the maximal univalent disk for the function R = q. This solves a p special case of the so-called Hermite-Biehler problem. 1
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