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Lecture Notes in Mathematics
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Lecture Notes in Mathematics
Johnson-Leung, Jennifer; Roberts, Brooks; Schmidt, Ralf
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.
Details
Published by: Springer
Publication Date: 2023-12-27
Format: Paperback
ISBN-13: 9783031451768
DOI: 10.1007/978-3-031-45177-5
Dimensions: 235cm x155cm
Pages: 362