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Synopsis
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:
- A detailed study of Pontrjagin’s dualtiy theorem.
- A thorough presentation of the cohomology of profinite groups.
- A introduction to simple algebras.
- An extensive discussion of the various ray class groups, both in the divisor-theoretic and the idelic language.
- The presentation of local and global class field theory in the algebra-theoretic concept of H. Hasse.
- The study of holomorphy domains and their relevance for class field theory.
- Simple classical proofs of the functional equation for L functions both for number fields and function fields.
- A self-contained presentation of the theorems of representation theory needed for Artin L functions.
- Application of Artin L functions for arithmetical results.
"synopsis" may belong to another edition of this title.
About the Author
Franz Halter-Koch is professor emeritus at the University of Graz, Graz, Austria. He is the author of Ideal Systems (Marcel Dekker,1998), Quadratic Irrationals (CRC, 2013), co-author of Non-Unique Factorizations (CRC 2006), and An Invitation to Algebraic Numbers and Algebraic Functions (CRC Press, 2020).
"About this title" may belong to another edition of this title.
- PublisherChapman and Hall/CRC
- Publication date2024
- ISBN 10 1032202653
- ISBN 13 9781032202655
- BindingPaperback
- LanguageEnglish
- Edition number1
- Number of pages584
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Class Field Theory and L Functions
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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: A detailed study of Pontrjagin's dualtiy theorem. A thorough presentation of the cohomology of profinite groups. A introduction to simple algebras. An extensive discussion of the various ray class groups, both in the divisor-theoretic and the idelic language. The presentation of local and global class field theory in the algebra-theoretic concept of H. Hasse.The study of holomorphy domains and their relevance for class field theory. Simple classical proofs of the functional equation for L functions both for number fields and function fields. A self-contained presentation of the theorems of representation theory needed for Artin L functions. Application of Artin L functions for arithmetical results. 586 pp. Englisch. Seller Inventory # 9781032202655
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