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Stable Klingen vectors and paramodular newforms

Record Type:	Electronic resources : Monograph/item
Title/Author:	Stable Klingen vectors and paramodular newformsby Jennifer Johnson-Leung, Brooks Roberts, Ralf Schmidt.
Author:	Johnson-Leung, Jennifer.
other author:	Roberts, Brooks.
Published:	Cham :Springer Nature Switzerland :2023.
Description:	xvii, 362 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Forms, Modular.
Online resource:	https://doi.org/10.1007/978-3-031-45177-5
ISBN:	9783031451775$q(electronic bk.)

Stable Klingen vectors and paramodular newforms
Johnson-Leung, Jennifer.

Stable Klingen vectors and paramodular newforms[electronic resource] /by Jennifer Johnson-Leung, Brooks Roberts, Ralf Schmidt. - Cham :Springer Nature Switzerland :2023. - xvii, 362 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23421617-9692 ;. - Lecture notes in mathematics ;2035..

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.

ISBN: 9783031451775$q(electronic bk.)

Standard No.: 10.1007/978-3-031-45177-5doiSubjects--Topical Terms:

272963
Forms, Modular.

LC Class. No.: QA243

Dewey Class. No.: 512.73

Stable Klingen vectors and paramodular newforms
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520 $a 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.
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