Hypergeometric functions in arithmetic geometry

Repository

Hypergeometric functions in arithmetic geometry

Show full record

Title: Hypergeometric functions in arithmetic geometry
Author: Salerno, Adriana Julia, 1979-
Abstract: 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 [mathematical symbol] on a certain family of hypersurfaces, [mathematical symbol] ([lamda]), 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.
Department: Mathematics
Subject: Hypergeometric functions Arithmetical algebraic geometry Hypersurfaces
URI: http://hdl.handle.net/2152/18410
Date: 2009-05

Files in this work

Download File: salernoa44324.pdf
Size: 429.2Kb
Format: application/pdf

This work appears in the following Collection(s)

Show full record


Advanced Search

Browse

My Account

Statistics

Information