English

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 pp-adic zeta values in the matrix entries of their pp-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 nn dimensions, in which case the Frobenius matrix entries are rational linear combinations of products of ζp(k)\zeta_p(k) with 1<k<n1 < k < n.

Keywords

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

R2 v1 2026-06-28T08:43:52.792Z