1. Frobenius structure and $p$-adic zeta function
- Author
-
Beukers, Frits and Vlasenko, Masha
- Subjects
Mathematics - Number Theory ,Mathematical Physics ,Mathematics - Algebraic Geometry - Abstract
For differential operators of Calabi-Yau type, Candelas, de la Ossa and van Straten conjecture the appearance of $p$-adic zeta values in the matrix entries of their $p$-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 $n$ dimensions, in which case the Frobenius matrix entries are rational linear combinations of products of $\zeta_p(k)$ with $1 < k < n$.
- Published
- 2023