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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2510.13469 |
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| _version_ | 1866909847740481536 |
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| author | Katre, S. A Krishnamurthi, Deepa |
| author_facet | Katre, S. A Krishnamurthi, Deepa |
| contents | It is known that every matrix of order n over the maximal order in an
algebraic number eld is a sum of k-th powers in various cases if a
discriminant condition is satis ed. It has been proved by Wadikar and
Katre that for every matrix of size 2 over maximal orders in rational
quaternion division algebras is a sum of squares and cubes. In this
paper we consider cyclic division algebras over Q of odd prime degree
and show that under some conditions every matrix of size greater equal 2 over these noncommutative rings is a sum of squares and a sum of cubes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13469 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matrices over maximal orders in cyclic division algebras over Q as sums of squares and cubes Katre, S. A Krishnamurthi, Deepa Number Theory It is known that every matrix of order n over the maximal order in an algebraic number eld is a sum of k-th powers in various cases if a discriminant condition is satis ed. It has been proved by Wadikar and Katre that for every matrix of size 2 over maximal orders in rational quaternion division algebras is a sum of squares and cubes. In this paper we consider cyclic division algebras over Q of odd prime degree and show that under some conditions every matrix of size greater equal 2 over these noncommutative rings is a sum of squares and a sum of cubes. |
| title | Matrices over maximal orders in cyclic division algebras over Q as sums of squares and cubes |
| topic | Number Theory |
| url | https://arxiv.org/abs/2510.13469 |