An adelic approach to the Kudla-Millson lifts over totally real number fields
Yingkun Li, Mingkuan Zhang, Riccardo Zuffetti
Source abstract
We compute the Fourier expansions of the Kudla-Millson theta lifts of vector-valued Hilbert cusp forms of parallel weight. These expansions are with respect to 0-dimensional cusps of non-compact orthogonal Shimura varieties defined over any totally real number field, and computed using a mixed model of the adelic Weil representation under a partial Fourier transform. As a consequence, we obtain the injectivity of the theta lifts under some additional hypothesis on the variety. Furthermore, we show that the theta lifts are square-integrable harmonic differential forms, and deduce lower bounds for dimensions of cohomology groups of such varieties.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.