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Negative Pisot Numbers from Alternating-Sign Characteristic Polynomials

Year: 2026

Type: article

Abstract: We study a family of characteristic polynomials with alternating signs for degreesn = 2 to 21. For every odd degree n ≥ 3 the polynomial has a unique negative real rootof modulus greater than one, while all other roots lie strictly inside the unit circle. Thesenumbers are therefore negative Pisot numbers. The moduli increase with n and convergeto 2 from below. This explicit infinite family complements earlier results of Hare andMossinghoff (2014) on negative Pisot numbers in the interval (−(1 +√5)/2,−1).

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.19003372

Authors: Helmdach, Emma, Helmdach, Emma

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7135200125

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