Exterior power sums

Yanping Luo, Ruiyi Yang, Keheng Zhu

arXiv:2607.22017v1 Primary: math.CO Secondary: math.NT

Abstract

We prove that for every fixed $λ>0$ and all sufficiently large $n$, any $z_1,\dots,z_n\in\C$ with $|z_j|\geq1$ satisfy $\max_{2\leq k\leq n+1}|\sum_j z_j^k|>e^{-λn}$. Consequently, the $n$th root of the optimal maximum tends to $1$, so no constant $C>1$ in Erdős 973 can exist. The proof combines a truncated exponential factorization with overconvergence on an open set outside the unit disk and a normal-family obstruction for Cauchy transforms.

Disclosure

“EXTERIOR POWER SUMS 7 Disclosure of automated assistance GPT-5.6 Sol was used during proof exploration, source comparison, and drafting. The written argument above is self-contained and does not use numerical computation or the output of a formal prover as a mathematical premise. A separate Lean 4 devel”
PDF page 7

Classification: Proof ideas or individual proof-step assistance
Multiplier: 8
Verified: 2026-08-23T19:04:39.131574Z

Structural counts

Pages 7 pdf

Theorems 1 source

Lemmas 5 source

Propositions 1 source

Corollaries 0 source

Definitions 0 source

Displayed equations 57 source

Bibliography entries 7 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file main__1_.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.