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Cyclotomic Binary Digit Hankel Zeros

Abstract

Cyclotomic Binary Digit Hankel Zeros

Theorem 1.1 (Cyclotomic Hankel zero characterization).

Lean statement: D5/S3/Combinatorics/DigitHankel/CyclotomicDigitHankel.result

Proof. Machine-checked in Lean as D5/S3/Combinatorics/DigitHankel/CyclotomicDigitHankel.result (✓ std3). ∎

Resolves. Problems/sobolewski-ulas-cyclotomic-hankel-zeros (proved) by D5/S3/Combinatorics/DigitHankel/CyclotomicDigitHankel.result.

Source. Repository-derived.

Acknowledgement. Bartosz Sobolewski, Maciej Ulas (2026). Hankel determinants of weighted binary sums of digits. DOI: 10.48550/arXiv.2607.09376. URL: https://arxiv.org/abs/2607.09376v1.

Commentary.

For every d at least two, every primitive d-th root of unity zeta, and every n at least two, the binary digit Hankel determinant at 2 times zeta is zero if and only if n lies in the cyclotomic zero intervals described by InZeroSet.

References