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Erdős problem / erdos

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Problem 513

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  1. vf_6fb4721c26311d5e

    theoretical

    Erdős Problem #513: declared status 'open'. Formalized: yes. Let f=∑n=0∞anznf=\sum_{n=0}^\infty a_nz^n be a transcendental entire function. What is the greatest possible value oflim inf⁡r→∞max⁡n∣anrn∣max⁡∣z∣=r∣f(z)∣?\liminf_{r\to \infty} \frac{\max_n\lvert a_nr^n\rvert}{\max_{\lvert z\rvert=r}\lvert f(z)\rvert}? Prize: no. Tags: analysis.

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