Johnson-Leung / Roberts / Schmidt Stable Klingen Vectors and Paramodular Newforms

1. Auflage 2023
ISBN: 978-3-031-45177-5
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 2342, 362 Seiten, eBook

Reihe: 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.

Zielgruppe

Research

Autoren/Hrsg.

Johnson-Leung, Jennifer

Roberts, Brooks

Schmidt, Ralf

Inhaltsverzeichnis

- Introduction. - 
Part I Local Theory.
- 2. Background. - 3. Stable Klingen Vectors. - 4. Some Induced Representations. - 5. Dimensions. - 6. Hecke Eigenvalues and Minimal Levels. - 7. The Paramodular Subspace. - 8. Further Results About Generic Representations. - 9. Iwahori-Spherical Representations. - 
Part II Siegel Modular Forms.
- 10. Background on Siegel Modular Forms. - 11. Operators on Siegel Modular Forms. - 12. Hecke Eigenvalues and Fourier Coefficients.

Über Autor(innen)

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.