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Generalized Poincare series for $mathrm{SU}(2,1)$

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 نشر من قبل Roelof W. Bruggeman
 تاريخ النشر 2021
  مجال البحث
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We define and study non-abelian Poincare series for the group $G=mathrm{SU} (2,1)$, i.e. Poincare series attached to a Stone-Von Neumann representation of the unipotent subgroup $N$ of $G$. Such Poincare series have in general exponential growth. In this study we use results on abelian and non-abelian Fourier term modules obtained in arXiv:1912.01334. We compute the inner product of truncations of these series and those associated to unitary characters of $N$ with square integrable automorphic forms, in connection with their Fourier expansions. As a consequence, we obtain general completeness results that, in particular, generalize those valid for the classical holomorphic (and antiholomorphic) Poincare series for $mathrm{SL}(2,mathbb{R})$.



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