Classifying minimal vanishing sums of roots of unity
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866918250674126848 |
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| author | Christie, Louis Dykema, Kenneth J. Klep, Igor |
| author_facet | Christie, Louis Dykema, Kenneth J. Klep, Igor |
| contents | A vanishing sum of roots of unity is called minimal if no proper, nonempty sub-sum of it vanishes. This paper classifies all minimal vanishing sums of roots of unity of weight at most 16 by hand, thereby uncovering new phenomena beyond the earlier 1998 classification of Poonen and Rubinstein (SIAM J. Discrete Math.) that went up to weight 12. The paper also develops an algorithm to explore higher weights up to 21, yielding a conjectural extension of the classification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_11268 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Classifying minimal vanishing sums of roots of unity Christie, Louis Dykema, Kenneth J. Klep, Igor Number Theory Rings and Algebras Primary 11L03, 11Y99, Secondary 11R18, 11T22 A vanishing sum of roots of unity is called minimal if no proper, nonempty sub-sum of it vanishes. This paper classifies all minimal vanishing sums of roots of unity of weight at most 16 by hand, thereby uncovering new phenomena beyond the earlier 1998 classification of Poonen and Rubinstein (SIAM J. Discrete Math.) that went up to weight 12. The paper also develops an algorithm to explore higher weights up to 21, yielding a conjectural extension of the classification. |
| title | Classifying minimal vanishing sums of roots of unity |
| topic | Number Theory Rings and Algebras Primary 11L03, 11Y99, Secondary 11R18, 11T22 |
| url | https://arxiv.org/abs/2008.11268 |