The theory of vector-modular forms for the modular group
Number Theory
2013-10-17 v1 High Energy Physics - Theory
Classical Analysis and ODEs
Abstract
We explain the basic ideas, describe with proofs the main results, and demonstrate the effectiveness, of an evolving theory of vector-valued modular forms (vvmf). To keep the exposition concrete, we restrict here to the special case of the modular group. Among other things,we construct vvmf for arbitrary multipliers, solve the Mittag-Leffler problem here, establish Serre duality and find a dimension formula for holomorphic vvmf, all in far greater generality than has been done elsewhere. More important, the new ideas involved are sufficiently simple and robust that this entire theory extends directly to any genus-0 Fuchsian group.
Keywords
Cite
@article{arxiv.1310.4458,
title = {The theory of vector-modular forms for the modular group},
author = {Terry Gannon},
journal= {arXiv preprint arXiv:1310.4458},
year = {2013}
}
Comments
38 pages