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Rigorous expansions of modular forms at CM points, I: Denominators by Xu, Chris is a scholarly article available to read on EtoBox.

What is Rigorous expansions of modular forms at CM points, I: Denominators about?

We describe an algorithm to rigorously compute the power series expansion at a CM point of a weight $2$ cusp form of level coprime to $6$. Our algorithm works by bounding the denominators that appear due to ramification, and without recourse to computing an explicit model of the corresponding modular curve. Our result is the first in a series of papers toward an eventual implementation of equationless Chabauty.

Author

Xu, Chris

Published

2025

Language

EN