A published paper or arXiv preprint answers the main question of Erdős Problem #973 (theorem erdos_973 in formal-conjectures) in full (proof, disproof, or the exact value asked for) with no hypotheses beyond the problem's own.

The problem, as stated in formal-conjectures (Apache 2.0):

Does there exist a constant C>1 such that, for every n\geq 2, there exists a sequence z_i\in \mathbb{C} with z_1=1 and \lvert z_i\rvert \geq 1 for all 1\leq i\leq n with \max_{2\leq k\leq n+1}\left\lvert \sum_{1\leq i\leq n}z_i^k\right\rvert < C^{-n}? This is Problem 7.3 in [Ha74], where it is attributed to Erdős. The answer is no, by Luo, Yang and Zhu [LYZ26] (and via the residual-polynomial method of Tan, Wang, Huang and Chen [TWHC26]): the maximum exceeds e^{-\lambda n} for every fixed \lambda>0 once n is large, so it decays subexponentially and no such C exists. See `erdos_973.variants.luo_yang_zhu` below.

References formal-conjectures lists for this problem (a starting point, not evidence):

• [Er92f] Erdős, L., On some problems of {P}. Turán concerning power sums of complex numbers. Acta Math. Hungar. (1992), 11--24.
• [Ha74] Hayman, W. K., Research problems in function theory: new problems. (1974), 155--180.
• [LYZ26] Luo, Yanping and Yang, Ruiyi and Zhu, Keheng, Exterior power sums. arxiv/2607.22017
• [TWHC26] Tan, Xiaojun and Wang, Qihang and Huang, Wei and Chen, Kun, Residual bounds for Schur-stable polynomials. arxiv/2608.02043
• [Tu84b] Turán, Paul, On a new method of analysis and its applications. (1984), xvi+584.
• PALOMAR-2026-09-20-000008