# What are you looking for?

Publications | Code |

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Graphics |

# (Pre)publications

For reprints (or rather

*electronic*reprints), just shoot me an email.# Notes & slides

• | Equidistribution of shapes of cubic fields of fixed quadratic resolvent | |

These are (expanded) slides from a 15-minute talk at CNTA XIV discussing my (upcoming) paper on the equidistribution of shapes of complex cubic fields with fixed trace-zero form on the corresponding geodesics in the modular curve. (The animations don't work in Preview on Mac.) | ||

• | Critical integers of motivic L-functions and Hodge numbers | |

This short note explains how to relate the critical integers of a motivic L-function (in the sense of Deligne) to the Hodge numbers of the motive. Specific examples are worked out (the Tate motive Q(1) and symmetric powers of modular forms). |

# Graphics

# Code

• | Overconvergent modular symbols code (including Hida theory): in progress | ||

This code is available here on github. See the arXiv. | |||

• | Iterate factorization trees: | ||

This code is available here on github. It was first written at the AIM workshop on the Galois theory of orbits in arithmetic dynamics and computes the
trees described in Section 3 of Rafe Jones and Nigel Boston's Settled polynomials over finite fields. | |||

• | Shape of a number field: | ||

This code is available here on github. It computes the "shape" of a number field. The shape of a number field K of degree n is the (n−1)-dimensional lattice in the Minkowski space given by the orthogonal complement of the vector 1. The output of this function is simply the (not necessarily reduced) Gram matrix of the lattice. | |||

• | Artin representations in Sage: in progress | ||

This code is available here on github. The goal of this project is to be able to compute with Artin representations in Sage. Some highlights include Artin conductors, L-functions, and root numbers. The project also improves the Galois group code to allow non-Galois fields. |

# Data

• | Quartic CM fields: up to discriminant 1×10^{6} | |

– CM_fields_degree_4.sobj, a Sage object containing the embedding of the maximal totally real subfield into the quartic CM field. | ||

– CM_fields_degree_4.txt, a text file containing data in the form of the pari group's nftables, i.e each line contains a 4-tuple whose entries are the discriminant, the coefficients of the defining polynomial, the class number, and the elementary divisors of the class group. | ||

• | Sextic CM fields: up to discriminant 2×10^{5} (there's only 4 of them!) | |

– CM_fields_degree_6.sobj, a Sage object containing the embedding of the maximal totally real subfield into the quartic CM field. | ||

– CM_fields_degree_6.txt, a text file containing data in the form of the pari group's nftables, i.e each line contains a 4-tuple whose entries are the discriminant, the coefficients of the defining polynomial, the class number, and the elementary divisors of the class group. |