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Miklós Schweitzer 1960- Problem 2

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November 18, 2015
college contestscomplex numbers

Problem Statement

2. Construct a sequence (an)n=1∞(a_n)_{n=1}^{\infty} of complex numbers such that, for every l>0l>0, the series
∑n=1∞∣an∣l\sum_{n=1}^{\infty} \mid a_n \mid ^{l}
be divergent, but for almost all θ\theta in (0,2π)(0,2\pi),
∏n=1∞(1+aneiθ)\prod_{n=1}^{\infty} (1+a_n e^{i\theta})
be convergent. (S. 11)
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