Building on the developments of many people including Evans, Greene, Katz, McCarthy,
Ono, Roberts, and Rodriguez-Villegas, we consider period functions for hypergeometric type …

Complex Ricci-flat (ie, Calabi-Yau) hypersurfaces in spaces admitting a maximal (toric) $ U
(1)^ n $ gauge symmetry of general type (encoded by certain non-convex and multi-layered …

We establish the supercongruences for the fourteen rigid hypergeometric Calabi–Yau
threefolds over Q conjectured by Rodriguez-Villegas in 2003. Our first method is based on …

We give an interim report on some improvements and generalizations of the Abbott–Kedlaya–
Roe method to compute the zeta function of a nondegenerate ample hypersurface in a …

We study the hypergeometric functions associated to five one-parameter deformations of
Delsarte K3 quartic hypersurfaces in projective space. We compute all of their Picard–Fuchs …

Full article: Special Hypergeometric Motives and Their L-Functions: Asai Recognition Skip to
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Abstract The Chevalley–Warning Theorem is a result on the solution set of a system of
polynomial equations f 1,…, fr in n variables over a finite field F q in the low degree case …

We use arithmetic and Hodge-theoretic techniques to study pencils of Calabi-Yau varieties
realized as highly symmetric hypersurfaces in Grassmannians and their quotients …

In this paper, we will study the connections between the mirror symmetry of K3 surfaces and
the geometry of the Legendre family of elliptic curves. We will prove that the mirror map of …

We study a family of hypergeometric motives $ H (\alpha,\beta| t) $ attached to a pair of
tuples $\alpha=(1/4, 1/2, 3/4) $, $\beta=(0, 0, 0) $. To each such motive we can attach a …