Computational Arithmetic of Modular Forms (Course notes)

2018/09/12 by Gabor Wiese, Wiese, Gabor
Computer Science · Mathematics · #11-01 #11F11 #11F25 #11F67 #11Y16 #Algebraic Geometry and Number Theory #Computational Geometry and Mesh Generation #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1809.04645

openalex publication_date 2018/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted student to implement it over any ring (such that a sufficient linear algebra theory is available in the chosen computer algebra system). The chosen approach is based on group cohomology and along the way the needed tools from homological algebra are provided.

Related

• Introduction to Modular Forms
• Hilbert modular forms and their applications
• Explicit computations of Siegel modular forms of degree two
• Computational aspects of modular forms and Galois representations
• Computing bases of modular forms using the graded algebra structure