ON THE COMPUTATION OF GENERAL VECTOR-VALUED MODULAR FORMS
Artikel i vetenskaplig tidskrift, 2023

We present and discuss an algorithm and its implementation that is capable of directly determining Fourier expansions of any vector-valued modular form of weight at least 2 associated with representations whose kernel is a congruence subgroup. It complements two available algorithms that are limited to inductions of Dirichlet characters and to Weil representations, thus covering further applications like Moonshine or Jacobi forms for congruence subgroups. We examine the calculation of invariants in specific representations via techniques from permutation groups, which greatly aids runtime performance. We explain how a generalization of cusp expansions of classical modular forms enters our implementation. After a heuristic consideration of time complexity, we relate the formulation of our algorithm to the two available ones, to high-light the compromises between level of generality and performance that each them makes.

Fourier expansions

cusp expansions

Holomorphic modular forms

Författare

Tobias Magnusson

Chalmers, Matematiska vetenskaper, Algebra och geometri

Martin Raum

Chalmers, Matematiska vetenskaper, Algebra och geometri

Mathematics of Computation

0025-5718 (ISSN) 1088-6842 (eISSN)

Vol. 92 344 2861-2891

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Ämneskategorier

Diskret matematik

DOI

10.1090/mcom/3847

Mer information

Senast uppdaterat

2023-10-06