Decidability of multiplicative matrix equations and related Diophantine problems
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909923610198016 |
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| author | Heintze, Sebastian Noubissie, Armand Tichy, Robert F. |
| author_facet | Heintze, Sebastian Noubissie, Armand Tichy, Robert F. |
| contents | Some new decidability results for multiplicative matrix equations over algebraic number fields are established. In particular, special instances of the so-called knapsack problem are considered. The proofs are based on effective methods for Diophantine problems in finitely generated domains as presented in the recent book of Evertse and Györy. The focus lies on explicit bounds for the size of the solutions in terms of heights as well as on bounds for the number of solutions. This approach also works for systems of symmetric matrices which do not form a semigroup. In the final section some related counting problems are investigated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03932 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decidability of multiplicative matrix equations and related Diophantine problems Heintze, Sebastian Noubissie, Armand Tichy, Robert F. Number Theory Some new decidability results for multiplicative matrix equations over algebraic number fields are established. In particular, special instances of the so-called knapsack problem are considered. The proofs are based on effective methods for Diophantine problems in finitely generated domains as presented in the recent book of Evertse and Györy. The focus lies on explicit bounds for the size of the solutions in terms of heights as well as on bounds for the number of solutions. This approach also works for systems of symmetric matrices which do not form a semigroup. In the final section some related counting problems are investigated. |
| title | Decidability of multiplicative matrix equations and related Diophantine problems |
| topic | Number Theory |
| url | https://arxiv.org/abs/2506.03932 |