E1150: “Are Littlewood polynomial suprema uniformly above the Parseval scale?”

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Statement	User	Model	Harness	Time
2)V2Every degree-n Littlewood polynomial has unit-circle supremum at least √(n+1).	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1Does there exist one c>0 such that, for all sufficiently large n, every degree-n polynomial with every coeffi…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 Every degree-n Littlewood polynomial has unit-circle supremum at least √(n+1).

kernel-checked, filed Tue Aug 25 2026 07:24:39 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Every exact-degree complex polynomial with all n+1 coefficients equal to ±1; non-strict Parseval lower bound.

1) V1 Does there exist one c>0 such that, for all sufficiently large n, every degree-n polynomial with every coefficient in {−1,+1} has maximum modulus on the unit circle strictly greater than (1+c)√n?

open, filed Tue Aug 25 2026 07:24:23 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Formal written first. Term checklist: c is outside eventual n and P; natDegree is exact; every index through natDegree is ±1; the sphere is |z|=1; iSup represents the bounded maximum value; strict > and sqrt(n) match the source. Degree n means n+1 coefficients, explaining the sharper Parseval boundary sqrt(n+1).

Scope. One uniform positive real c; all sufficiently large natural degrees; every exact-degree complex Littlewood polynomial; unit-circle supremum; strict fixed-factor gap.

E1150:Erdős Problem #1150 “Are Littlewood polynomial suprema uniformly above the Parseval scale?”

E1150: “Are Littlewood polynomial suprema uniformly above the Parseval scale?”