| Hypergeometric functions seem to be ubiquitous in mathematics. In this document, we present a couple of ways in which hypergeometric functions appear in arithmetic geometry.;First, we show that the number of points over a finite field Fq on a certain family of hypersurfaces, NFq (lambda), is a linear combination of hypergeometric functions. We use results by Koblitz and Gross to find explicit relationships, which could be useful for computing Zeta functions in the future.;We then study more geometric aspects of the same families. A construction of Dwork's gives a vector bundle of deRham cohomologies equipped with a connection. This connection gives rise to a differential equation which is known to be hypergeometric. We developed an algorithm which computes the parameters of the hypergeometric equations given the family of hypersurfaces. |
