Stable Klingen vectors and paramodular newforms / Jennifer Johnson-Leung, Brooks Roberts, Ralf Schmidt.

Format:

Book

Author/Creator:

Johnson-Leung, Jennifer, author.

Roberts, Brooks, 1964- author.

Schmidt, Ralf, 1968- author.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 0075-8434 2342.

Lecture notes in mathematics, 0075-8434 ; volume 2342

Language:

English

Subjects (All):

Forms, Modular.

Eigenvalues.

Fourier analysis.

Physical Description:

xvii, 359 pages : illustrations ; 24 cm.

Place of Publication:

Cham : Springer, [2023]

Summary:

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.

Notes:

Includes bibliographical references (pages 351-356) and index.

ISBN:

9783031451768

3031451767

OCLC:

1418966300