Asymptotics of $n$-universal lattices over number fields
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918179369910272 |
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| author | Park, Dayoon Visser, Robin Yatsyna, Pavlo Yoon, Jongheun |
| author_facet | Park, Dayoon Visser, Robin Yatsyna, Pavlo Yoon, Jongheun |
| contents | We prove an explicit asymptotic formula for the logarithm of the minimal ranks of $n$-universal lattices over the ring of integers of totally real number fields. We also show that, for any constant $C > 0$ and $n \geq 3$, there are only finitely many totally real fields with an $n$-universal lattice of rank at most $C$, with all such fields being effectively computable. Similarly, for any $n \geq 3$, we show that there are only finitely many totally real fields admitting an $n$-universal criterion set of size at most $C$, with all such fields likewise being effectively computable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26652 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotics of $n$-universal lattices over number fields Park, Dayoon Visser, Robin Yatsyna, Pavlo Yoon, Jongheun Number Theory 11E12 (Primary) 11R80, 11N45 (Secondary) We prove an explicit asymptotic formula for the logarithm of the minimal ranks of $n$-universal lattices over the ring of integers of totally real number fields. We also show that, for any constant $C > 0$ and $n \geq 3$, there are only finitely many totally real fields with an $n$-universal lattice of rank at most $C$, with all such fields being effectively computable. Similarly, for any $n \geq 3$, we show that there are only finitely many totally real fields admitting an $n$-universal criterion set of size at most $C$, with all such fields likewise being effectively computable. |
| title | Asymptotics of $n$-universal lattices over number fields |
| topic | Number Theory 11E12 (Primary) 11R80, 11N45 (Secondary) |
| url | https://arxiv.org/abs/2510.26652 |