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

Georgios Papas

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

Number Theory 2026-03-23 v2

Authors: Georgios Papas

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.

Keywords

G-functions abelian varieties elliptic curves CM points p-adic values

Cite

@article{arxiv.2510.11814,
  title  = {On the $v$-adic values of G-functions II},
  author = {Georgios Papas},
  journal= {arXiv preprint arXiv:2510.11814},
  year   = {2026}
}

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