Stable Klingen Vectors and Paramodular Newforms

Johnson-Leung, Jennifer, Roberts, Brooks, Schmidt, Ralf

Stable Klingen Vectors and Paramodular Newforms
  • 出版商: Springer
  • 出版日期: 2023-12-27
  • 售價: $2,830
  • 貴賓價: 9.5 折 $2,689
  • 語言: 英文
  • 頁數: 362
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031451767
  • ISBN-13: 9783031451768

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相關主題

商品描述

This book describes a novel approach to the study of Siegel modular forms of degree two with paramodular level. It introduces the family of stable Klingen congruence subgroups of GSp(4) and uses this family to obtain new relations between the Hecke eigenvalues and Fourier coefficients of paramodular newforms, revealing a fundamental dichotomy for paramodular representations. Among other important results, it includes a complete description of the vectors fixed by these congruence subgroups in all irreducible representations of GSp(4) over a nonarchimedean local field.
Siegel paramodular forms have connections with the theory of automorphic representations and the Langlands program, Galois representations, the arithmetic of abelian surfaces, and algorithmic number theory. Providing a useful standard source on the subject, the book will be of interest to graduate students and researchers working in the above fields.

商品描述(中文翻譯)

本書描述了一種對具有參模級數的二階Siegel模形式的研究的新方法。它介紹了GSp(4)的穩定Klingen同餘子群家族，並利用這個家族獲得了參模新形式的Hecke特徵值和傅立葉係數之間的新關係，揭示了參模表示的基本二分法。除了其他重要結果外，它還完整描述了在非阿基米德局部場上的所有不可約表示中，這些同餘子群所固定的向量。
Siegel參模形式與自守表示和Langlands計劃的理論、Galois表示、阿貝爾曲面的算術以及算法數論有關。作為該主題的有用標準資源，本書將對從事上述領域的研究的研究生和研究人員感興趣。

作者簡介

Jennifer Johnson-Leung is a professor in the Department of Mathematics and Statistical Science at the University of Idaho. She received her PhD from the California Institute of Technology in 2005. Her research focuses on Siegel modular forms, Iwasawa theory, and special values of L-functions.
Brooks Roberts is a member of the Department of Mathematics and Statistical Science at the University of Idaho. He received his PhD from the University of Chicago in 1992. He is a co-author of the book Local Newforms for GSp(4) (Springer). His research focuses on Siegel modular forms, representation theory, and the theta correspondence.
Ralf Schmidt is a professor in the Department of Mathematics at the University of North Texas. He received his PhD from Hamburg University in 1998. He is a co-author of the books Transfer of Siegel Cusp Forms of Degree 2 (Memoirs of the AMS), LocalNewforms for GSp(4) (Springer), and Elements of the Representation Theory of the Jacobi Group (Birkhäuser). His research focuses on Siegel modular forms and representation theory.

作者簡介(中文翻譯)

Jennifer Johnson-Leung是愛達荷大學數學與統計科學系的教授。她於2005年在加州理工學院獲得博士學位。她的研究專注於Siegel模形式、岩澤理論和L-函數的特殊值。

Brooks Roberts是愛達荷大學數學與統計科學系的成員。他於1992年在芝加哥大學獲得博士學位。他是書籍《Local Newforms for GSp(4)》（Springer）的合著者。他的研究專注於Siegel模形式、表示論和theta對應。

Ralf Schmidt是北德克薩斯大學數學系的教授。他於1998年在漢堡大學獲得博士學位。他是書籍《Transfer of Siegel Cusp Forms of Degree 2》（AMS的論文集）、《Local Newforms for GSp(4)》（Springer）和《Elements of the Representation Theory of the Jacobi Group》（Birkhäuser）的合著者。他的研究專注於Siegel模形式和表示論。

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