Stable Klingen Vectors and Paramodular Newforms - Jennifer Johnson-Leung, Brooks Roberts, Ralf Schmidt

Stable Klingen Vectors and Paramodular Newforms

Buch | Softcover
XVII, 362 Seiten
2023 | 1st ed. 2023
Springer International Publishing (Verlag)
978-3-031-45176-8 (ISBN)
69,54 inkl. MwSt
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.

lt;b>Jennifer Johnson-Leung is a professor in the Department of Mathematics and Statistical Science at the University of Idaho. She received her PhD from the California Institute of Technology in 2005. Her research focuses on Siegel modular forms, Iwasawa theory, and special values of L-functions.
Brooks Roberts is a member of the Department of Mathematics and Statistical Science at the University of Idaho. He received his PhD from the University of Chicago in 1992. He is a co-author of the book Local Newforms for GSp(4) (Springer). His research focuses on Siegel modular forms, representation theory, and the theta correspondence.
Ralf Schmidt is a professor in the Department of Mathematics at the University of North Texas. He received his PhD from Hamburg University in 1998. He is a co-author of the books Transfer of Siegel Cusp Forms of Degree 2 (Memoirs of the AMS), Local Newforms for GSp(4) (Springer), and Elements of the Representation Theory of the Jacobi Group (Birkhäuser). His research focuses on Siegel modular forms and representation theory.

- Introduction. - Part I Local Theory. - 2. Background. - 3. Stable Klingen Vectors. - 4. Some Induced Representations. - 5. Dimensions. - 6. Hecke Eigenvalues and Minimal Levels. - 7. The Paramodular Subspace. - 8. Further Results About Generic Representations. - 9. Iwahori-Spherical Representations. - Part II Siegel Modular Forms. - 10. Background on Siegel Modular Forms. - 11. Operators on Siegel Modular Forms. - 12. Hecke Eigenvalues and Fourier Coefficients.

Erscheinungsdatum
Reihe/Serie Lecture Notes in Mathematics
Zusatzinfo XVII, 362 p.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 581 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Arithmetik / Zahlentheorie
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Schlagworte Fourier Coefficients of Paramodular Newforms • Fourier Coefficients of Siegel Modular Newforms • Hecke Eigenvalues for Paramodular Newforms • Hecke Eigenvalues for Siegel Modular Forms • Hecke Operators on Siegel Modular Forms • Klingen Vectors • Level Lowering Operators • Paramodular Hecke Operators • Representations of GSp(4) • Representation Theory of GSp(4) • Siegel modular forms • Siegel Modular Forms with Paramodular Level • Siegel Modular Newforms • Stable Klingen Vectors
ISBN-10 3-031-45176-7 / 3031451767
ISBN-13 978-3-031-45176-8 / 9783031451768
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