Logarithmic coefficients of close-to-convex functions

2016/08/26 by Ali, Md Firoz, Thomas, D. K., Vasudevarao, A.
#30C45 #30C55 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1608.07520

Abstract

For an analytic and univalent function f in the unit disk \mathbbD:=\z∈ℂ:|z|<1\ with the normalization f(0)=0=f'(0)-1, the logarithmic coefficients γ_n are defined by log (f(z))/(z)= 2∑_n=1^∞ γ_n zⁿ. In the present paper, we consider the class of close-to-convex functions (with argument 0), and determine the sharp upper bound of |γ₃| for such functions f, which proves a recent conjecture of the first and third authors [1].

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