Representations of Su(2,1) in Fourier Term Modules

Bruggeman, Roelof W., Miatello, Roberto J.

Representations of Su(2,1) in Fourier Term Modules
  • 出版商: Springer
  • 出版日期: 2023-11-07
  • 售價: $2,410
  • 貴賓價: 9.5 折 $2,290
  • 語言: 英文
  • 頁數: 210
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 303143191X
  • ISBN-13: 9783031431913

    • 海外代購書籍(需單獨結帳)

相關主題

商品描述

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.

商品描述(中文翻譯)

本書研究自守形式的傅立葉展開中出現的模組，即 SU(2,1) 上的傅立葉項模組，這是一個具有非阿貝爾單群的最小一階李群。它考慮了與 SU(2,1) 的最大單群的特徵相關的「阿貝爾」傅立葉項模組，以及通過 theta 函數描述的「非阿貝爾」模組。給出了所有傅立葉項模組的子模結構的完整描述，並討論了對自守形式的傅立葉展開以及具有指數增長的自守形式的影響。
這些結果可以應用於證明平方可積自守形式空間中的 Poincaré 級數的完備性結果。
本書針對對自守形式、李群上的調和分析以及與 Poincaré 級數相關的數論主題感興趣的研究人員和研究生，同時也作為傅立葉-雅可比係數的譜展開的基本參考資料。只需具備李群及其表示的背景知識。

作者簡介

Roelof W. Bruggeman was born in Zwolle, the Netherlands. He obtained his PhD at Utrecht University in 1972, and was a postdoctoral fellow at Yale University (1972-73). He has worked at Utrecht University since 1980, now as a guest after his retirement in 2005. In 2022 he became a corresponding member of the Academia Nacional de Ciencias in Córdoba, Argentina. The main research themes in his work are the spectral theory of Maass forms, the study of families of automorphic forms as a function of complex parameters, and the relation between automorphic forms and cohomology.
Roberto J. Miatello was born in Buenos Aires, Argentina. After studying at FaMAF, UNCordoba, Argentina (1965-1970) he obtained his PhD from Rutgers University in 1976. He was a professor at UFPe, Brazil (1977-1980), a member of the IAS, Princeton, USA (1980-81), and has been a professor at FaMAF (UNC) since 1982, becoming Professor Emeritus in 2016. He is a member of Conicet and (since 1996) the National Academy of Sciences of Argentina. His research focuses on geometry, the spectral theory of locally symmetric varieties, and automorphic forms.

作者簡介(中文翻譯)

Roelof W. Bruggeman出生於荷蘭的Zwolle。他於1972年在烏特勒支大學獲得博士學位，並在1972年至1973年間在耶魯大學擔任博士後研究員。自1980年以來，他一直在烏特勒支大學工作，現在已退休並擔任客座教授。2022年，他成為阿根廷科爾多瓦國家科學院的對應會員。他的主要研究方向包括Maass形式的譜理論、自守形式家族的研究以及自守形式與上同調之間的關係。

Roberto J. Miatello出生於阿根廷的布宜諾斯艾利斯。在阿根廷科爾多瓦國立科學與數學學院（FaMAF, UNCordoba）就讀（1965-1970）後，他於1976年在羅格斯大學獲得博士學位。他曾任巴西聯邦大學（UFPe）教授（1977-1980），普林斯頓高級研究院（IAS）成員（1980-1981），並自1982年起擔任阿根廷科爾多瓦國立科學與數學學院（FaMAF, UNC）教授，並於2016年成為名譽教授。他是阿根廷科學與技術研究委員會（Conicet）和阿根廷國家科學院（自1996年起）的成員。他的研究主要集中在幾何學、局部對稱變量的譜理論和自守形式。

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