Abstract
We consider functionals L which are the real parts of linear combinations of two Taylor coefficients on the class S of holomorphic univalent functions in the unit disk. The Bombieri conjecture can be interpreted in the form that L are locally maximized by the Koebe function simultaneously on S and on its subclass \(S_R\) consisting of typically real functions. We derive necessary criteria for the Bombieri conjecture in terms of inequalities for solutions to systems of differential equations in variations for the Loewner ODE.
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This work is supported by the Russian Science Foundation under Grant 17-11-01229
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In memory of Alexander Vasil’ev.
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Prokhorov, D. Necessary criteria for the Bombieri conjecture. Anal.Math.Phys. 8, 679–690 (2018). https://doi.org/10.1007/s13324-018-0248-2
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DOI: https://doi.org/10.1007/s13324-018-0248-2