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Abstract: We show that for a monic polynomial p of degree d, the length of the levelset {z: |pz|=1} is at most 9.2 d, which improves an earlier estimate due toP. 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 extremalpolynomial this level set is connected.



Author: Alexandre Eremenko aand Walter Hayman

Source: https://arxiv.org/







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