This survey paper attempts to present in as elementary a way as possible a wide panorama
of results concerning the relations between differential equations on the one hand and …

In this thesis we will study Feynman integrals from the perspective of A-hypergeometric
functions, a generalization of hypergeometric functions which goes back to Gelfand …

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

We consider the fourteen families W of Calabi–Yau threefolds with one complex structure
parameter and Picard–Fuchs equation of hypergeometric type, like the mirror of the quintic …

Based on Ramanujan's theories of elliptic functions to alternative bases, commutative formal
group laws, and supercongruence techniques, including the residue-sum technique, we …

In the 1980's, Greene defined {\it hypergeometric functions over finite fields} using Jacobi
sums. The framework of his theory establishes that these functions possess many properties …

We survey the archimedean representations and Langlands parameters corresponding to
holomorphic Siegel modular forms of degree~ 2. This leads to a determination of …

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 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 …

Full article: Special Hypergeometric Motives and Their L-Functions: Asai Recognition Skip to
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