An arithmetic characterization of some algebraic functions and a new proof of an algebraicity prediction by Golyshev
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916550497271808 |
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| author | Bostan, Alin |
| author_facet | Bostan, Alin |
| contents | We provide a new arithmetic characterization for the sequence of coefficients of algebraic power series $f(t)$ having the property that the differential equation $y'(t) = f(t) y(t)$ has algebraic solutions only. This extends a recent result by Delaygue and Rivoal, and also provides a new and shorter proof of an algebraicity result predicted by Golyshev. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13951 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An arithmetic characterization of some algebraic functions and a new proof of an algebraicity prediction by Golyshev Bostan, Alin Number Theory We provide a new arithmetic characterization for the sequence of coefficients of algebraic power series $f(t)$ having the property that the differential equation $y'(t) = f(t) y(t)$ has algebraic solutions only. This extends a recent result by Delaygue and Rivoal, and also provides a new and shorter proof of an algebraicity result predicted by Golyshev. |
| title | An arithmetic characterization of some algebraic functions and a new proof of an algebraicity prediction by Golyshev |
| topic | Number Theory |
| url | https://arxiv.org/abs/2408.13951 |