Stable Klingen Vectors and Paramodular Newforms
Stable Klingen Vectors and Paramodular Newforms
English | 2023 | ISBN: 3031451767 | 361 Pages | PDF EPUB (True) | 46 MB
English | 2023 | ISBN: 3031451767 | 361 Pages | PDF EPUB (True) | 46 MB
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.