- 376 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
eBook - ePub
About this book
The book contains the main results of class field theory and Artin L functions, both for number fields and function fields, together with the necessary foundations concerning topological groups, cohomology, and simple algebras.
While the first three chapters presuppose only basic algebraic and topological knowledge, the rest of the books assumes knowledge of the basic theory of algebraic numbers and algebraic functions, such as those contained in my previous book, An Invitation to Algebraic Numbers and Algebraic Functions (CRC Press, 2020).
The main features of the book are:
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- A detailed study of Pontrjagin's dualtiy theorem.
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- A thorough presentation of the cohomology of profinite groups.
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- A introduction to simple algebras.
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- An extensive discussion of the various ray class groups, both in the divisor-theoretic and the idelic language.
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- The presentation of local and global class field theory in the algebra-theoretic concept of H. Hasse.
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- The study of holomorphy domains and their relevance for class field theory.
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- Simple classical proofs of the functional equation for L functions both for number fields and function fields.
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- A self-contained presentation of the theorems of representation theory needed for Artin L functions.
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- Application of Artin L functions for arithmetical results.
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Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access Class Field Theory and L Functions by Franz Halter-Koch in PDF and/or ePUB format, as well as other popular books in Mathematics & Algebra. We have over one million books available in our catalogue for you to explore.
Information
Table of contents
- Cover Page
- Half-Title Page
- Title Page
- Copyright Page
- Dedication Page
- Contents
- Preface
- Author
- Notation
- 1 Topological groups and infinite Galois theory
- 2 Cohomology of groups
- 3 Simple algebras
- 4 Local class field theory
- 5 Global fields: Adeles, ideles and holomorphy domains
- 6 Global class field theory
- 7 Functional equations and Artin L functions
- Bibliography
- Subject Index
- List of Symbols