Stable Klingen Vectors and Paramodular Newforms

Jennifer Johnson-Leung, Brooks Roberts, Ralf Schmidt

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English

Springer International Publishing AG
27 December 2023

Groups & group theory; Number theory; Calculus & mathematical analysis

Series: Lecture Notes in Mathematics

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.

By: Jennifer Johnson-Leung, Brooks Roberts, Ralf Schmidt
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 1st ed. 2023
Volume: 2342
Dimensions: Height: 235mm, Width: 155mm,
Weight: 581g
ISBN: 9783031451768
ISBN 10: 3031451767
Series: Lecture Notes in Mathematics
Pages: 362
Publication Date: 27 December 2023
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

Reviews for Stable Klingen Vectors and Paramodular Newforms

“The book is well structured, beginning with an introductory chapter that provides an overview of the topic and explains the main results.” (Riccardo Zuffetti, Mathematical Reviews, August, 2025)