{"product_id":"representations-of-su2-1-in-fourier-term-modules","title":"Representations of SU(2,1) in Fourier Term Modules","description":"This book studies the modules arising in Fourier expansions of automorphic forms, namely Fourier term modules on SU(2,1), the smallest rank one Lie group 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 modules is given, with a discussion of the consequences for Fourier expansions of automorphic forms, automorphic forms with exponential growth included.   These results can be  applied to prove a completeness result for Poincaré series in spaces of square integrable automorphic forms.   Aimed at researchers and graduate students interested in automorphic forms, harmonic analysis on Lie groups, and number-theoretic topics related to Poincaré series, the book will also serve as a basic reference on spectral expansion with Fourier-Jacobi coefficients. Only a background in Lie groups and their representations is assumed.","brand":"Gardners","offers":[{"title":"Default Title","offer_id":57492320518517,"sku":"9783031431913","price":49.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0612\/7193\/3106\/files\/9783031431913.jpg?v=1786529155","url":"https:\/\/backstory.london\/products\/representations-of-su2-1-in-fourier-term-modules","provider":"Backstory","version":"1.0","type":"link"}