Wednesday, October 25
Milner 317,
12:30 PM
Title: Weierstrass
Polynomials on X_0(p)
Abstract: Weierstrass
points are special geometrically defined points that exist on any
algebraic curve of genus 2 or higher. On a modular curve, we define the
Weierstrass polynomial to be the one with roots at the j(Q) for any
Weierstrass point Q (or, more generally, with roots at $\phi(Q)$, where
$\phi$ is a (weight zero) modular function on X_0(m)). In this talk, we
study some of the arithmetic properties of these polynomials and the
fields they generate.