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# Texas A&M Number Theory Seminar

##
Department of Mathematics

Milner 317

Wednesdays, 12:30-1:30 PM

Ahmad
El-Guindy

Texas A&M University

**Wednesday, October 25**

**Milner 317,****
12:30 PM**

**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.