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arXiv · 2609.12148

An adelic approach to the Kudla-Millson lifts over totally real number fields

Yingkun Li·Mingkuan Zhang·Riccardo Zuffetti
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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.

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Yingkun Li, Mingkuan Zhang, Riccardo Zuffetti. 2026-09-10. An adelic approach to the Kudla-Millson lifts over totally real number fields. https://arxiv.org/abs/2609.12148

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