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Stable Klingen Vectors and Paramodular Newforms de Jennifer Johnson-Leung

Stable Klingen Vectors and Paramodular Newforms: Lecture Notes in Mathematics, cartea 2342

Autor Jennifer Johnson-Leung, Brooks Roberts, Ralf Schmidt
en Limba Engleză Paperback – 27 dec 2023
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.
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Specificații

ISBN-13: 9783031451768
ISBN-10: 3031451767
Pagini: 362
Ilustrații: XVII, 362 p.
Dimensiuni: 155 x 235 mm
Greutate: 0.54 kg
Ediția:1st ed. 2023
Editura: Springer Nature Switzerland
Colecția Springer
Seria Lecture Notes in Mathematics

Locul publicării:Cham, Switzerland

Cuprins

- 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.

Notă biografică

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), LocalNewforms 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.

Textul de pe ultima copertă

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.

Caracteristici

Introduces an important new family of congruence subgroups of GSp(4) Reveals a new dichotomy for paramodular representations Connects Fourier coefficients and Hecke eigenvalues of paramodular newforms