Stable Klingen Vectors and Paramodular Newforms: 2342 (Lecture Notes in Mathematics, 2342) - Softcover

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

 
9783031451768: Stable Klingen Vectors and Paramodular Newforms: 2342 (Lecture Notes in Mathematics, 2342)
Softcover
ISBN 10: 3031451767 ISBN 13: 9783031451768
Publisher: Springer, 2023

Synopsis

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.

"synopsis" may belong to another edition of this title.

About the Author

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.

From the Back Cover

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.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2023
Language
English
ISBN 10 
3031451767
ISBN 13 
9783031451768
Binding
Paperback
Edition number
1
Number of pages
379