Coefficients of multivalent symmetric functions of bounded boundary rotation (Q1896381)

The authors prove that \(m\)-fold symmetric \(p\)-valent functions \(f(z) = z^p + \sum^\infty_{k = 1} a_k z^{mk + p}\) of boundary rolation \(\leq k \pi\) are close-to-convex of order \(p (k/2 - 1)/m\), i.e. \[ V_p (k,m) \subset C_p \left( {p(k/2 - 1) \over m}, m \right), \] extending the reviewer's result for \(p = 1 \) [Proc. Am. Math. Soc. 105, No. 2, 324-329 (1989; Zbl 0669.30007)]. As a consequence a sharp coefficient estimate for functions \(f \in V_p (k,m)\) is deduced.