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Titlebook: An Introduction to Automorphic Representations; With a view toward t Jayce R. Getz,Heekyoung Hahn Textbook 2024 Springer Nature Switzerland

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發(fā)表于 2025-3-21 18:02:25 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
期刊全稱An Introduction to Automorphic Representations
期刊簡(jiǎn)稱With a view toward t
影響因子2023Jayce R. Getz,Heekyoung Hahn
視頻videohttp://file.papertrans.cn/156/155142/155142.mp4
發(fā)行地址Provides a detailed yet accessible introduction to the Langlands Program.Covers advanced topics that are rarely treated in textbooks, ex. the trace formula and Galois representations.Serves as a highl
學(xué)科分類Graduate Texts in Mathematics
圖書(shū)封面Titlebook: An Introduction to Automorphic Representations; With a view toward t Jayce R. Getz,Heekyoung Hahn Textbook 2024 Springer Nature Switzerland
影響因子.The goal of this textbook is to introduce and study automorphic representations, objects at the very core of the Langlands Program. It is designed for use as a primary text for either a semester or a year-long course, for the independent study of advanced topics, or as a reference for researchers. The reader is taken from the beginnings of the subject to the forefront of contemporary research.? The journey provides an accessible gateway to one of the most fundamental areas of modern mathematics, with deep connections to arithmetic geometry, representation theory, harmonic analysis, and mathematical physics..The first part of the text is dedicated to developing the notion of automorphic representations. Next, it states a rough version of the Langlands functoriality conjecture, motivated by the description of unramified admissible representations of reductive groups over nonarchimedean local fields.?The next chapters develop the theory necessary to make the Langlands functoriality conjecture precise.? Thus supercuspidal representations are defined locally, cuspidal representations and Eisenstein series are defined globally, and Rankin-Selberg .L-.functions are defined to give a link
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沙發(fā)
發(fā)表于 2025-3-21 23:04:52 | 只看該作者
Representations of Totally Disconnected Groups, state the general definition of an automorphic representation in the next chapter. At the end of the chapter, we prove Flath’s theorem. This fundamental result implies that automorphic representations of a global field can be factored, in a suitable sense, along the places of the field.
板凳
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地板
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978-3-031-42610-0Springer Nature Switzerland AG 2024
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發(fā)表于 2025-3-22 12:00:00 | 只看該作者
6#
發(fā)表于 2025-3-22 13:33:33 | 只看該作者
Representations of Totally Disconnected Groups, state the general definition of an automorphic representation in the next chapter. At the end of the chapter, we prove Flath’s theorem. This fundamental result implies that automorphic representations of a global field can be factored, in a suitable sense, along the places of the field.
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發(fā)表于 2025-3-22 19:10:33 | 只看該作者
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https://doi.org/10.1007/978-3-658-41648-5The arithmetic objects of interest in this book are constructed using global fields and their adele rings. We briefly summarize the construction of the adeles in this section; references include [CF86, Neu99, RV99].
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發(fā)表于 2025-3-23 01:32:04 | 只看該作者
https://doi.org/10.1007/978-3-658-41648-5In this chapter, we introduce the main players in the representation theory of real Lie groups. In particular, we define admissible representations, .-modules and infinitesimal characters. The chapter ends with a brief discussion of the Langlands classification.
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發(fā)表于 2025-3-23 08:50:18 | 只看該作者
https://doi.org/10.1007/978-3-658-41648-5In this chapter, we define automorphic forms and use them to give the general definition of an automorphic representation. We then explain the relationship between discrete automorphic representations and automorphic representations.
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