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商品詳細
Stable Klingen Vectors and Paramodular Newforms. 1st ed. 2023.
・ISBN 978-3-031-45176-8 paper EUR 64.99
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| 著者・編者 | Johnson-Leung, Jennifer / Roberts, Brooks / Schmidt, Ralf, |
|---|---|
| シリーズ | Lecture Notes in Mathematics |
| 出版社 | (Springer International Publishing AG, SZ) |
| 出版年月 | 2023 |
| ページ数 | 362 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-924＞ |
解説
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.
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.