Geodesic
The sum of coefficients of bounded univalent functions
Matematičeskie zametki, Tome 61 (1997) no. 5, pp. 728-733

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We solve the maximal value problem for the functional $\operatorname{Re}\sum_{j=1}^ma_{k_j}$ in the class of functions $f(z)=z+a_2z^2+\dotsb$ that are holomorphic and univalent in the unit disk and satisfy the inequality $|f(z)|$. We prove that the Pick functions are extremal for this problem for sufficiently large $M$ whenever the set of indices $k_1,\dots,k_m$ contains an even number. 
@article{MZM_1997_61_5_a9,
     author = {D. V. Prokhorov},
     title = {The sum of coefficients of bounded univalent functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {728--733},
     publisher = {mathdoc},
     volume = {61},
     number = {5},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_5_a9/}
}
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D. V. Prokhorov. The sum of coefficients of bounded univalent functions. Matematičeskie zametki, Tome 61 (1997) no. 5, pp. 728-733. http://geodesic.mathdoc.fr/item/MZM_1997_61_5_a9/