WeilConjectures 2006-03-03 16:17:03 2008-06-09 10:20:49 Conjecture % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here Conjectures made by Weil on the form of the zeta function of a variety over a finite field. Specifically he thought it should be rational, it should split into polynomial parts with integral coefficients, with roots of a certain magnitude, and of degree = Betti number. Further there should be a functional equation. (Flesh this out ;))