Taylor Expansions of Modular Forms at CM Points
Thesis PDF (DOI ethz-b-000646162)
Implementation (GitHub)
Uses the method of Zagier-Villegas to demonstrate that the Taylor coefficients of the $j$-invariant is non-vanishing at the CM points $\zeta_{-3}, \zeta_{-4}$. Presents a general (Sagemath) implementation for computing periodic and non-vanishing behaviour of Taylor coefficients of arbitrary modular forms at the CM points $\zeta_{-3}, \zeta_{-4}$.