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arXiv · 2510.11814

On the $v$-adic values of G-functions II

Georgios Papas
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Abstract

This is the second paper in a series by the author, centered on the study of values of G-functions associated to a $1$-parameter family of abelian varieties $f:\CX\rightarrow S$ and a point $s_0\in S(K)$ over some number field $K$. Here we study the case where $f:\CX\rightarrow S$ is a family of elliptic curves. Extending work of Andr\'e and Beukers, we construct relations among the values of G-functions in this setting at points whose fibers are CM elliptic curves.

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Georgios Papas. 2025-10-13. On the $v$-adic values of G-functions II. https://arxiv.org/abs/2510.11814

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