Claims

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1968_01_01_herzog_piranian: Herzog and Piranian construct a non-monomial entire function whose number of maximum modulus points on the circle of radius r is unbounded as r grows, answering the first question of Problem 1117 affirmatively; credited by the site.

2026_09_05_gu: Qiyuan Gu's manuscript, written with GPT-6 Astra, claims that a non-monomial entire function has at most 2k maximum modulus points on all but countably many circles, so the second question of Problem 1117 has a negative answer.

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