The Dwork Family and Hypergeometric Functions

Details The Dwork Family and Hypergeometric Functions The Dwork Family and Hypergeometric Functions

2012-02-22

arxiv.org/abs/1202.5008v1

Mathematics

Number Theory

Scientific paper

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 were not only useful to Dwork in his study of his deformation theory for computing Zeta functions of families, but they have also proven to be extremely useful to physicists working in mirror symmetry. A startling result is that these families are very closely linked to hypergeometric functions. This phenomenon was carefully studied by Dwork and Candelas, de la Ossa, and Rodr\'{i}guez-Villegas in a few special cases. Dwork, Candelas, et.al. observed that, for these families, the differential equation associated to the Gauss-Manin connection is in fact hypergeometric. We have developed a computer algorithm, implemented in Pari-GP, which can check this result for more cases by computing the Gauss-Manin connection and the parameters of the hypergeometric differential equation.

Affiliated with

Also associated with

No associations

Rating

The Dwork Family and Hypergeometric Functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Dwork Family and Hypergeometric Functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Dwork Family and Hypergeometric Functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-416927