Some application of Grunsky coefficients in the theory of univalent functions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866909625557712896 |
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| author | Obradović, Milutin Tuneski, Nikola |
| author_facet | Obradović, Milutin Tuneski, Nikola |
| contents | Let function $f$ be normalized, analytic and univalent in the unit disk ${\mathbb D}=\{z:|z|<1\}$ and $f(z)=z+\sum_{n=2}^{\infty} a_n z^n$. Using a method based on Grusky coefficients we study several problems over that class of univalent functions: upper bounds of the special case of the generalised Zalcman conjecture $|a_2a_3-a_4|$, of the third logarithmic coefficient, and of the second Hankel determinant for the logarithmic coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_11945 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Some application of Grunsky coefficients in the theory of univalent functions Obradović, Milutin Tuneski, Nikola Complex Variables 30C45, 30C50, 30C55 Let function $f$ be normalized, analytic and univalent in the unit disk ${\mathbb D}=\{z:|z|<1\}$ and $f(z)=z+\sum_{n=2}^{\infty} a_n z^n$. Using a method based on Grusky coefficients we study several problems over that class of univalent functions: upper bounds of the special case of the generalised Zalcman conjecture $|a_2a_3-a_4|$, of the third logarithmic coefficient, and of the second Hankel determinant for the logarithmic coefficients. |
| title | Some application of Grunsky coefficients in the theory of univalent functions |
| topic | Complex Variables 30C45, 30C50, 30C55 |
| url | https://arxiv.org/abs/2009.11945 |