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The ternary
cyclotomic polynomials $\Phi_{3pq}$
Alexandre Benoist and Antonella Perucca |
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Vol. 19 (2026), No. 1, 51–72
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Abstract |
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Cyclotomic polynomials are a classical and fundamental topic in number theory, and still an active field of research. The aim of this work is providing a formula for the family of ternary cyclotomic polynomials , where are prime numbers greater than such that and . We can derive various properties from our formula. In particular, we prove a conjecture of Zhang on the number of maximum gaps for the coefficients. |
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Keywords
cyclotomic polynomials, ternary cyclotomic polynomials,
maximum gap, number of coefficients
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Mathematical Subject Classification
Primary: 11C08
Secondary: 11Y99
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Milestones
Received: 5 July 2023
Revised: 13 May 2024
Accepted: 25 August 2024
Published: 25 January 2026
Communicated by Amanda Folsom
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Authors |
| Alexandre Benoist | |
| Department of Mathematics University of Luxembourg Esch-sur-Alzette Luxembourg |
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| Antonella Perucca | |
| Department of Mathematics University of Luxembourg Esch-sur-Alzette Luxembourg |
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| © 2026 MSP (Mathematical Sciences Publishers). |
