Titlebook: Representations of SU(2,1) in Fourier Term Modules; Roelof W. Bruggeman,Roberto J. Miatello Book 2023 The Editor(s) (if applicable) and Th

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Introduction,book. We summarize the main results on Fourier term modules in four theorems. We give an overview of applications to automorphic forms, considering also automorphic forms with moderate exponential growth.

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The Lie Group SU(2,1) and Subgroups,aratory chapter, we fix a standard realization . of ., and consider the representation theory of the maximal unipotent subgroup . and of the maximal compact subgroup . in an Iwasawa decomposition .. We need to understand the realizations of irreducible representations of . and of . in spaces of func

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Application to Automorphic Forms,rms are required to have at most polynomial growth at the cusps. Here we also define automorphic forms with moderate exponential growth. A growth condition on the modular form implies properties of the Fourier expansion. For ., an automorphic form with Fourier terms that have polynomial growth has p

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Book 2023oup with a non-abelian unipotent subgroup. It considers the “abelian” Fourier term modules connected to characters of the maximal unipotent subgroups of SU(2,1), and also the “non-abelian” modules, described via theta functions. A complete description of the submodule structure of all Fourier term m

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Application to Automorphic Forms,ition on the modular form implies properties of the Fourier expansion. For ., an automorphic form with Fourier terms that have polynomial growth has polynomial growth itself. For . this does not necessarily hold..We consider also the Fourier expansion of families of automorphic forms, and of generating vectors of irreducible automorphic modules.