Class Field Theory and L Functions

Foundations and Main Results

Franz Halter-Koch (University of Graz, Austria)

$147

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English

Chapman & Hall/CRC
26 August 2024

Algebra; Number theory; Probability & statistics

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.

By: Franz Halter-Koch (University of Graz Austria)
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 1.080kg
ISBN: 9781032202655
ISBN 10: 1032202653
Pages: 564
Publication Date: 26 August 2024
Audience: General/trade , ELT Advanced
Format: Paperback
Publisher's Status: Forthcoming

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).