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Weierstrass Points on Hyperelliptic Shimura Curves
Chaos, Holly Paige
Chaos, Holly Paige
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Abstract
Roughly speaking, Weierstrass points are certain special points defined on curves of genus $\geq 2$, and modular curves are curves whose points parametrize objects of interest. For this reason, it is natural to be curious about what can be said about Weierstrass points on modular curves. Work was done in this direction by Rohrlich and Ahlgren-Ono for classical modular curves, and by Vincent for Drinfeld modular curves. In this dissertation we present results on the Weierstrass points of hyperelliptic Shimura curves $X_0^D(p)$ for $p$ prime, and when $X_0^D(1)$ has genus zero. As these are the very first results on Weierstrass points in this setting we hope this work will spur further study of more general cases.
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2025-01-01