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arXiv · 2609.27609

Construction of vector-valued adelic automorphic forms

Oliver Stein
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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.

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Oliver Stein. 2026-09-23. Construction of vector-valued adelic automorphic forms. https://arxiv.org/abs/2609.27609

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