Transcendence criteria for infinite products of algebraic numbers
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910855536312320 |
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| author | Laursen, Mathias L. |
| author_facet | Laursen, Mathias L. |
| contents | Using an application of Schmidt's Subspace Theorem, this paper gives new transcendence criteria for rapidly converging infinite products of algebraic numbers. The paper also improves existing criteria for irrationality of products and criteria for irrationality and transcendence of infinite series. These results generalize a classical theorem on the irrationality of infinite series due to Erdős. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01575 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Transcendence criteria for infinite products of algebraic numbers Laursen, Mathias L. Number Theory 11J81, 11J87 Using an application of Schmidt's Subspace Theorem, this paper gives new transcendence criteria for rapidly converging infinite products of algebraic numbers. The paper also improves existing criteria for irrationality of products and criteria for irrationality and transcendence of infinite series. These results generalize a classical theorem on the irrationality of infinite series due to Erdős. |
| title | Transcendence criteria for infinite products of algebraic numbers |
| topic | Number Theory 11J81, 11J87 |
| url | https://arxiv.org/abs/2503.01575 |