| dc.description.abstract | Until 1949, studying the number of points on an algebraic variety over a finite field
did not seem as worthwhile as it is today, but when André Weil proposed his Weil
Conjectures, linking the number of points over a finite field to certain topological
properties of an algebraic variety over C via the zeta function, mathematicians have
not only occupied themselves with proving these conjectures, but also with finding
feasible methods to compute the zeta function and consequently derive the associated
topological properties. In this thesis, we will focus on the methods of the proof
of rationality of the zeta function, found by Bernard Dwork in 1960. We will study
these methods -along with other theories by Dwork- which we can use to derive
new ways of computing the zeta function, which allows us to derive a new method
to compute the zeta function of a non-degenerate hypersurface. | |
