Necessary criteria for the Bombieri conjecture
type: Item
instance of: scholarly article
title: Necessary criteria for the Bombieri conjecture
zbMATH Open document ID: 1423.30019
published in: Analysis and Mathematical Physics
publication date: 2019-01-11T00:00:00Z
review text: In the paper under review the author considers functionals \(L\) which are the real parts of linear combinations of two Taylor coefficients in the class \(S\) of holomorphic univalent functions \(f(z)=z+\sum_{n=2}^{\infty}a_{n}z^{n}\) in the unit disk. These are related with the Bombieri conjecture in the following way. The Bombieri conjecture can be interpreted in the form that \(L\) are locally maximized by the Koebe function simultaneously in the class \(S\) and on its subclass \(S_{R}\) consisting of typically real functions. The author derives necessary criteria for the Bombieri conjecture in terms of inequalities for solutions to systems of differential equations in variations for the Loewner ODE.
reviewed by: Stamatis Pouliasis
Mathematics Subject Classification ID: 30C80
Mathematics Subject Classification ID: 30C20
Mathematics Subject Classification ID: 30C25
zbMATH DE Number: 7000060
zbMATH Keywords: Bombieri conjecture
zbMATH Keywords: Loewner equation
zbMATH Keywords: maximum principle
zbMATH Keywords: Hamilton function
author: Dmitri V. Prokhorov
MaRDI profile type: Publication
full work available at URL: s13324-018-0248-2
OpenAlex ID: W2890545147
Wikidata QID: Q123076243
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DOI: 10.1007/S13324-018-0248-2
description: scientific article; zbMATH DE number 7000060