Stable Klingen Vectors and Paramodular Newforms

Beschreibung

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.
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.
Introduces an important new family of congruence subgroups of GSp(4) Reveals a new dichotomy for paramodular representations Connects Fourier coefficients and Hecke eigenvalues of paramodular newforms

Autor*in

Jennifer Johnson-Leung

Themen in »Stable Klingen Vectors and Paramodular Newforms«

Siegel Modular Forms Siegel Modular Newforms Siegel Modular Forms with Paramodular Level Stable Klingen Vectors Klingen Vectors Paramodular Hecke Operators Hecke Operators on Siegel Modular Forms Hecke Eigenvalues for Paramodular Newforms Hecke Eigenvalues for Siegel Modular Forms Fourier Coefficients of Paramodular Newforms Fourier Coefficients of Siegel Modular Newforms Level Lowering Operators Representations of GSp(4) Representation Theory of GSp(4)

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“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)

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