The exceptional set in Cassel's theorem on small cyclotomic integers
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915824029138944 |
|---|---|
| author | Bajpai, Jitendra Das, Srijan Kedlaya, Kiran S. Le, Nam H. Lee, Meghan Leudière, Antoine Mello, Jorge |
| author_facet | Bajpai, Jitendra Das, Srijan Kedlaya, Kiran S. Le, Nam H. Lee, Meghan Leudière, Antoine Mello, Jorge |
| contents | In a 1965 paper, R. Robinson made five conjectures about the classification of cyclotomic algebraic integers for which the maximum absolute value in any complex embedding (the house) is small, modulo the equivalence relation generated by Galois conjugation and multiplication by roots of unity. In response to one of these conjectures, Cassels showed in 1969 that when the house is at most $\sqrt{5}$, one obtains three parametric families plus an effectively computable finite set of equivalence classes of exceptions. Building on the work of Jones, Calegari-Morrison-Snyder, and Robinson-Wurtz, we determine this exceptional set. By specializing to the case where the house is strictly less than 2, we resolve the final outstanding conjecture from Robinson's 1965 paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20435 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The exceptional set in Cassel's theorem on small cyclotomic integers Bajpai, Jitendra Das, Srijan Kedlaya, Kiran S. Le, Nam H. Lee, Meghan Leudière, Antoine Mello, Jorge Number Theory Primary 11R18, secondary 11R06, 11Y40 In a 1965 paper, R. Robinson made five conjectures about the classification of cyclotomic algebraic integers for which the maximum absolute value in any complex embedding (the house) is small, modulo the equivalence relation generated by Galois conjugation and multiplication by roots of unity. In response to one of these conjectures, Cassels showed in 1969 that when the house is at most $\sqrt{5}$, one obtains three parametric families plus an effectively computable finite set of equivalence classes of exceptions. Building on the work of Jones, Calegari-Morrison-Snyder, and Robinson-Wurtz, we determine this exceptional set. By specializing to the case where the house is strictly less than 2, we resolve the final outstanding conjecture from Robinson's 1965 paper. |
| title | The exceptional set in Cassel's theorem on small cyclotomic integers |
| topic | Number Theory Primary 11R18, secondary 11R06, 11Y40 |
| url | https://arxiv.org/abs/2510.20435 |