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Stable Klingen vectors and paramodul...

Johnson-Leung, Jennifer.

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Stable Klingen vectors and paramodular newforms

Record Type:	Electronic resources : Monograph/item
Title/Author:	Stable Klingen vectors and paramodular newforms/ by 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

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 ;v. 2342..

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

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

540521
Forms, Modular.

LC Class. No.: QA243

Dewey Class. No.: 512.73

Stable Klingen vectors and paramodular newforms
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245 1 0 $a Stable Klingen vectors and paramodular newforms $h [electronic resource] / $c by Jennifer Johnson-Leung, Brooks Roberts, Ralf Schmidt.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2023.
300 $a xvii, 362 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 1617-9692 ; $v v. 2342
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.
650 0 $a Forms, Modular. $3 540521
650 0 $a Eigenvalues. $3 631789
650 0 $a Fourier analysis. $3 532730
650 1 4 $a Number Theory. $3 891078
650 2 4 $a Topological Groups and Lie Groups. $3 3593340
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 891107
700 1 $a Roberts, Brooks. $3 3756317
700 1 $a Schmidt, Ralf. $3 3756318
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Lecture notes in mathematics ; $v v. 2342. $3 3756319
856 4 0 $u https://doi.org/10.1007/978-3-031-45177-5
950 $a Mathematics and Statistics (SpringerNature-11649)