Class Field Theory and L Functions

Foundations and Main Results

Franz Halter-Koch (University of Graz, Austria)

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Hardback

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English

CRC Press
17 May 2022

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: CRC Press
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 1.000kg
ISBN: 9781138583580
ISBN 10: 1138583588
Pages: 564
Publication Date: 17 May 2022
Audience: College/higher education , General/trade , Primary , ELT Advanced
Format: Hardback
Publisher's Status: Active

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).