Computing fundamental domains for the Bruhat{Tits tree for GL 2(Qp), p-adic automorphic forms, and the canonical embedding of Shimura curves

Cameron Franc, Marc Masdeu

Research output: Contribution to journalArticleResearchpeer-review

7 Citations (Scopus)

Abstract

We describe algorithms that allow the computation of fundamental domains in the Bruhat-Tits tree for the action of discrete groups arising from quaternion algebras. These algorithms are used to compute spaces of rigid modular forms of arbitrary even weight, and we explain how to evaluate such forms to high precision using overconvergent methods. Finally, these algorithms are applied to the calculation of conjectural equations for the canonical embedding of p-adically uniformizable rational Shimura curves. We conclude with an example in the case of a genus 4 Shimura curve.

Original languageEnglish
Pages (from-to)1-23
Number of pages23
JournalLMS Journal of Computation and Mathematics
Volume17
Issue number1
DOIs
Publication statusPublished - Apr 2014

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