On a theorem of Rickards
Preprint <pdf|arxiv>
James Rickards proved that
the generating series of intersection numbers of real quadratic
geodesics on indefinite Shimura curves are elliptic modular forms. We
reinterpret this as a Kudla—Millson theta series, and prove that his
generating series is the diagonal restriction of a Hilbert modular
form, analogous to results of Darmon—Pozzi—Vonk and Branchereau.
Modular algorithms for Gross-Stark units and Stark-Heegner points
Contemp. Math., vol. 796, 2024, Amer. Math. Soc., Providence, RI, 261-284 <journal|arxiv>
Algorithms for computing Gross-Stark units and Stark-Heegner points using overconvergent modular forms, with implementations
in magma and sage.
Diagonal Restrictions of Hilbert Modular Forms
DPhil Thesis, University of Oxford, 2024 <pdf>
We extend the results of [DPV21] to ring class characters, or equivalently, to values
of analytic theta cocycles at non-fundamental RM points. The
main contribution is an explicit adelic construction of Hilbert
Eisenstein series transforming with respect to SL2(𝒪) where 𝒪
is a non-maximal order in a real quadratic field.
drawspec
A simple script building on pytikz to draw the spectrum of the ring of integers in a number field. Conveniently, this also generates tikz code for use in LaTeX documents. A version of this is included in the LMFDB, see example and slides.
typst-preview.el
An Emacs package for live preview of Typst, a modern LaTeX alternative.
tree-sitter-sage
A tree-sitter grammar for SageMath, which is a slight modification of tree-sitter-python.
tree-sitter-magma
A tree-sitter grammar for the magma computer algebra system.
WCLvsSCL
Some code for computing the probabilistic zeta function of a finite poset lattice. Includes code which disproves a conjecture in (a previous version of) arxiv:2112.13766.