Logarithmic coefficients of close-to-convex functions

Abstract

For an analytic and univalent function $f$ in the unit disk $\mathbb{D}:=\{z\in \mathbb{C}:|z|<1\}$ with the normalization $f(0)=0=f^{\prime }(0)-1$, the logarithmic coefficients ${\gamma }_n$ are defined by $\log \frac{f(z)}{z}=2{\sum }_{n=1}^{\infty }{\gamma }_n{z}^n$. In the present paper, we consider the class of close-to-convex functions (with argument $0$), and determine the sharp upper bound of $|{\gamma }_3|$ for such functions $f$, which proves a recent conjecture of the first and third authors [1].

This paper has been withdrawn by the author due to a error in the proof

References in corpus (1)

• Logarithmic coefficients of some close-to-convex functions