2023
DOI: 10.48550/arxiv.2301.11160
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Estimates of Picard modular cusp forms

Abstract: In this article, for n ≥ 2, we compute asymptotic, qualitative, and quantitative estimates of the Bergman kernel of Picard modular cusp forms associated to torsion-free, cocompact subgroups of SU (n, 1), C . The main result of the article is the following result. Let Γ ⊂ SU (2, 1), OK be a torsion-free subgroup of finite index, where K is a totally imaginary field. Let B k Γ denote the Bergman kernel associated to the S k (Γ), complex vector space of weight-k cusp forms with respect to Γ. Let B 2 denote the 2-… Show more

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