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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2008
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/0805.2295 |
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| _version_ | 1866917622872801280 |
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| author | Eremenko, Alexandre Hayman, Walter |
| author_facet | Eremenko, Alexandre Hayman, Walter |
| contents | We show that for a monic polynomial p of degree d, the length of the level set {z: |p(z)|=1} is at most 9.2 d, which improves an earlier estimate due to P. Borwein. For d=2 we show that the extremal level set is the Bernoullis' Lemniscate. One ingredient of our proofs is the fact that for an extremal polynomial this level set is connected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0805_2295 |
| institution | arXiv |
| publishDate | 2008 |
| record_format | arxiv |
| spellingShingle | On the length of lemniscates Eremenko, Alexandre Hayman, Walter Complex Variables 30C10 We show that for a monic polynomial p of degree d, the length of the level set {z: |p(z)|=1} is at most 9.2 d, which improves an earlier estimate due to P. Borwein. For d=2 we show that the extremal level set is the Bernoullis' Lemniscate. One ingredient of our proofs is the fact that for an extremal polynomial this level set is connected. |
| title | On the length of lemniscates |
| topic | Complex Variables 30C10 |
| url | https://arxiv.org/abs/0805.2295 |