Some code written as part of my mathematical research, also available on
GitHub
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Rigid meromorphic cocycles
Henri Darmon and I wrote a Magma package to compute spaces of rigid meromorphic cocycles,
as introduced in our papers
- Singular moduli for real quadratic fields (Duke Math. J. 2021)
- Arithmetic intersections of modular geodesics (J. Number Theory 2022)
- Real quadratic Borcherds products (Pure Appl. Math. Q. 2022)
It computes rigid meromorphic theta cocycles, their RM values, their cuspidal values, as well as
Stark-Heegner points on elliptic curves.
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Overconvergent modular forms
This code builds on the code of Alan Lauder, and some parts of it were also written jointly with him.
It has three main branches, which compute:
- Spaces of overconvergent modular forms for any prime p, as well as routines
to compute eigenforms, projections, and Chow-Heegner points on elliptic curves.
Computing overconvergent forms for small primes (LMS J. Comp. 2015)
- Spaces of overconvergent modular forms at the boundary of weight space.
Modular eigenforms at the boundary of weight space (Res. Number Theory 2018)
- p-Adic L-functions of totally real fields (with A. Lauder).
Computing p-adic L-functions of totally real fields (Math. Comp. 2022)
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Quadratic Chabauty
The following code, building crucially on code written by Jan Tuitman, is based on the following papers with Jennifer Balakrishnan, Netan Dogra,
Steffen Müller, and Jan Tuitman
- Explicit Chabauty-Kim for the non-split Cartan modular curve of level 13 (Ann. Math. 2019)
- Quadratic Chabauty for modular curves (Submitted)