On the $v$-adic values of G-functions III
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915570039914496 |
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| author | Papas, Georgios |
| author_facet | Papas, Georgios |
| contents | In this third part in this series we continue from \cite{papaspadicpart1}, the study of relations among values of G-functions associated to a $1$-parameter family of principally polarized abelian surfaces. In particular, we establish relations among the values of these G-functions, in both the archimedean and $p$-adic setting, at points corresponding to abelian surfaces with Quaternionic multiplication. We also discuss applications to the Zilber-Pink conjecture in $\mathcal{A}_2$ that naturally follow from our discussion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19683 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the $v$-adic values of G-functions III Papas, Georgios Number Theory Algebraic Geometry In this third part in this series we continue from \cite{papaspadicpart1}, the study of relations among values of G-functions associated to a $1$-parameter family of principally polarized abelian surfaces. In particular, we establish relations among the values of these G-functions, in both the archimedean and $p$-adic setting, at points corresponding to abelian surfaces with Quaternionic multiplication. We also discuss applications to the Zilber-Pink conjecture in $\mathcal{A}_2$ that naturally follow from our discussion. |
| title | On the $v$-adic values of G-functions III |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2510.19683 |