Frobenius structure and $p$-adic zeta values
Number Theory
2025-09-18 v3 Mathematical Physics
Algebraic Geometry
math.MP
Abstract
For differential operators of Calabi-Yau type, Candelas, de la Ossa and van Straten conjecture the appearance of -adic zeta values in the matrix entries of their -adic Frobenius structure expressed in the standard basis of solutions near a MUM-point. We prove that this phenomenon holds for simplicial and hyperoctahedral families of Calabi-Yau hypersurfaces in dimensions, in which case the Frobenius matrix entries are rational linear combinations of products of with .
Cite
@article{arxiv.2302.09603,
title = {Frobenius structure and $p$-adic zeta values},
author = {Frits Beukers and Masha Vlasenko},
journal= {arXiv preprint arXiv:2302.09603},
year = {2025}
}
Comments
This is the final version, incorporating minor updates to the text