8 papers · 1 filter
Hypergeometric decomposition of Delsarte K3 pencils
Rachel Davis, Jessamyn Dukes, Thais Gomes Ribeiro +4
We study five pencils of projective quartic Delsarte K3 surfaces. Over finite fields, we give explicit formulas for the point counts of each family, written in terms of hypergeomet…
Hasse--Witt matrices and mirror toric pencils
Adriana Salerno, Ursula Whitcher
Mirror symmetry suggests unexpected relationships between arithmetic properties of distinct families of algebraic varieties. For example, Wan and others have shown that for some mi…
Hypergeometric decomposition of symmetric K3 quartic pencils
Charles F. Doran, Tyler L. Kelly, Adriana Salerno +3
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…
Zeta functions of alternate mirror Calabi-Yau families
Charles F. Doran, Tyler L. Kelly, Adriana Salerno +3
We prove that if two Calabi-Yau invertible pencils have the same dual weights, then they share a common factor in their zeta functions. By using Dwork cohomology, we demonstrate th…
Origami Constructions of Rings of Integers of Imaginary Quadratic Fields
Juergen Kritschgau, Adriana Salerno
In the making of origami, one starts with a piece of paper, and through a series of folds along seed points one constructs complicated three-dimensional shapes. Mathematically, one…
The Dwork Family and Hypergeometric Functions
Adriana Salerno
In his work studying the Zeta functions of families of hypersurfaces, Dwork came upon a one-parameter family of hypersurfaces (now known as \emph{the} Dwork family). These examples…
Counting Points over Finite Fields and Hypergeometric Functions
Adriana Salerno
It is a well known result that the number of points over a finite field on the Legendre family of elliptic curves can be written in terms of a hypergeometric function modulo . I…
Igusa class polynomials, embeddings of quartic CM fields, and arithmetic intersection theory
Helen Grundman, Jennifer Johnson-Leung, Kristin Lauter +3
Bruinier and Yang conjectured a formula for an intersection number on the arithmetic Hilbert modular surface, CM(K).T_m, where CM(K) is the zero-cycle of points corresponding to ab…