PreprintarXiv licencearXiv
Construction of vector-valued adelic automorphic forms
Abstract
We construct an adelic counterpart of Scheithauer's lifting map from scalar-valued modular forms to vector-valued modular forms transforming with the Weil representation. More precisely, we introduce suitable spaces of vector-valued adelic automorphic forms and define an adelic lifting map between the corresponding scalar-valued and vector-valued automorphic forms. We then prove that this adelic construction is compatible with Scheithauer's classical lifting map under adelization. In this way, the relation between scalar-valued and vector-valued modular forms is transferred naturally to the adelic setting.
Related
- Free modules of vector-valued modular forms and applications to Jacobi forms
- Vector-Valued Wavelet Bases as Hilbert 𝕄m(ℝ)-Module Bases: A Construction from Scalar Wavelets
- Vertex operator algebra bundles on Riemann surfaces of higher genus and automorphic forms for Fuchsian groups
- Harder's conjecture and Hermitian automorphic forms
- Characteristic Classes of Adelic Vector Bundles and Applications
BibTeX
@misc{stein2026construction,
title = {{Construction of vector-valued adelic automorphic forms}},
author = {Oliver Stein},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27609},
eprint = {2609.27609},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27609},
}
RIS
TY - UNPB
TI - Construction of vector-valued adelic automorphic forms
AU - Oliver Stein
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27609
UR - https://arxiv.org/abs/2609.27609
AB - We construct an adelic counterpart of Scheithauer's lifting map from scalar-valued modular forms to vector-valued modular forms transforming with the Weil representation. More precisely, we introduce suitable spaces of vector-valued adelic automorphic forms and define an adelic lifting map between the corresponding scalar-valued and vector-valued automorphic forms. We then prove that this adelic construction is compatible with Scheithauer's classical lifting map under adelization. In this way, the relation between scalar-valued and vector-valued modular forms is transferred naturally to the adelic setting.
ER -