Franz Halter-Koch's Books

Class Field Theory and L Functions

Foundations and Main Results

By: Franz Halter-Koch

Write a review Read reviews Take a Quiz Solve Book Puzzle

Class Field Theory and L Functions

Foundations and Main Results

By: Franz Halter-Koch

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.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

585

Publisher

CRC Press

Published Date

ISBN 10

0429014732

ISBN 13

9780429014734

Quadratic Irrationals

An Introduction to Classical Number Theory

By: Franz Halter-Koch

Write a review Read reviews Take a Quiz Solve Book Puzzle

Quadratic Irrationals

An Introduction to Classical Number Theory

By: Franz Halter-Koch

Quadratic Irrationals: An Introduction to Classical Number Theory gives a unified treatment of the classical theory of quadratic irrationals. Presenting the material in a modern and elementary algebraic setting, the author focuses on equivalence, continued fractions, quadratic characters, quadratic orders, binary quadratic forms, and class groups.T

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

431

Publisher

CRC Press

Published Date

ISBN 10

1466591846

ISBN 13

9781466591844

Ideal Systems

An Introduction to Multiplicative Ideal Theory

By: Franz Halter-Koch

Write a review Read reviews Take a Quiz Solve Book Puzzle

Ideal Systems

An Introduction to Multiplicative Ideal Theory

By: Franz Halter-Koch

Provides for the first time a concise introduction to general and multiplicative ideal theory, valid for commutative rings and monoids and presented in the language of ideal systems on (commutative) monoids.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

444

Publisher

CRC Press

Published Date

ISBN 10

0824701860

ISBN 13

9780824701864

An Invitation To Algebraic Numbers And Algebraic Functions

By: Franz Halter-Koch

Write a review Read reviews Take a Quiz Solve Book Puzzle

An Invitation To Algebraic Numbers And Algebraic Functions

By: Franz Halter-Koch

The author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions which both in its conception and in many details differs from the current literature on the subject. The basic features are: Field-theoretic preliminaries and a detailed presentation of Dedekind’s ideal theory including non-principal orders and various types of class groups; the classical theory of algebraic number fields with a focus on quadratic, cubic and cyclotomic fields; basics of the analytic theory including the prime ideal theorem, density results and the determination of the arithmetic by the class group; a thorough presentation of valuation theory including the theory of difference, discriminants, and higher ramification. The theory of function fields is based on the ideal and valuation theory developed before; it presents the Riemann-Roch theorem on the basis of Weil differentials and highlights in detail the connection with classical differentials. The theory of congruence zeta functions and a proof of the Hasse-Weil theorem represent the culminating point of the volume. The volume is accessible with a basic knowledge in algebra and elementary number theory. It empowers the reader to follow the advanced number-theoretic literature, and is a solid basis for the study of the forthcoming volume on the foundations and main results of class field theory. Key features: • A thorough presentation of the theory of Algebraic Numbers and Algebraic Functions on an ideal and valuation-theoretic basis. • Several of the topics both in the number field and in the function field case were not presented before in this context. • Despite presenting many advanced topics, the text is easily readable. Franz Halter-Koch is professor emeritus at the university of Graz. He is the author of “Ideal Systems” (Marcel Dekker,1998), “Quadratic Irrationals” (CRC, 2013), and a co-author of “Non-Unique Factorizations” (CRC 2006).

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

595

Publisher

CRC Press

Published Date

ISBN 10

0429014678

ISBN 13

9780429014673

Non-Unique Factorizations

Algebraic, Combinatorial and Analytic Theory

By: Alfred Geroldinger,Franz Halter-Koch

Write a review Read reviews Take a Quiz Solve Book Puzzle

Non-Unique Factorizations

Algebraic, Combinatorial and Analytic Theory

By: Alfred Geroldinger,Franz Halter-Koch

From its origins in algebraic number theory, the theory of non-unique factorizations has emerged as an independent branch of algebra and number theory. Focused efforts over the past few decades have wrought a great number and variety of results. However, these remain dispersed throughout the vast literature. For the first time, Non-Unique Factoriza

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

723

Publisher

CRC Press

Published Date

ISBN 10

1420003208

ISBN 13

9781420003208

Class Field Theory and L Functions

Foundations and Main Results

By: Franz Halter-Koch

Write a review Read reviews Take a Quiz Solve Book Puzzle

Class Field Theory and L Functions

Foundations and Main Results

By: Franz Halter-Koch

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

425

Publisher

CRC Press

Published Date

ISBN 10

0429014724

ISBN 13

9780429014727

Reciprocity Laws

From Euler to Eisenstein

By: Franz Lemmermeyer

Write a review Read reviews Take a Quiz Solve Book Puzzle

Reciprocity Laws

From Euler to Eisenstein

By: Franz Lemmermeyer

This book covers the development of reciprocity laws, starting from conjectures of Euler and discussing the contributions of Legendre, Gauss, Dirichlet, Jacobi, and Eisenstein. Readers knowledgeable in basic algebraic number theory and Galois theory will find detailed discussions of the reciprocity laws for quadratic, cubic, quartic, sextic and octic residues, rational reciprocity laws, and Eisensteins reciprocity law. An extensive bibliography will be of interest to readers interested in the history of reciprocity laws or in the current research in this area.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

503

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662128934

ISBN 13

9783662128930

An Invitation To Algebraic Numbers And Algebraic Functions

By: Franz Halter-Koch

Write a review Read reviews Take a Quiz Solve Book Puzzle

An Invitation To Algebraic Numbers And Algebraic Functions

By: Franz Halter-Koch

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

595

Publisher

CRC Press

Published Date

ISBN 10

0429014678

ISBN 13

9780429014673

Quadratic Irrationals

An Introduction to Classical Number Theory

By: Franz Halter-Koch

Write a review Read reviews Take a Quiz Solve Book Puzzle

Quadratic Irrationals

An Introduction to Classical Number Theory

By: Franz Halter-Koch

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

431

Publisher

CRC Press

Published Date

ISBN 10

1466591846

ISBN 13

9781466591844

Quadratic Number Fields

By: Franz Lemmermeyer

Write a review Read reviews Take a Quiz Solve Book Puzzle

Quadratic Number Fields

By: Franz Lemmermeyer

This undergraduate textbook provides an elegant introduction to the arithmetic of quadratic number fields, including many topics not usually covered in books at this level. Quadratic fields offer an introduction to algebraic number theory and some of its central objects: rings of integers, the unit group, ideals and the ideal class group. This textbook provides solid grounding for further study by placing the subject within the greater context of modern algebraic number theory. Going beyond what is usually covered at this level, the book introduces the notion of modularity in the context of quadratic reciprocity, explores the close links between number theory and geometry via Pell conics, and presents applications to Diophantine equations such as the Fermat and Catalan equations as well as elliptic curves. Throughout, the book contains extensive historical comments, numerous exercises (with solutions), and pointers to further study. Assuming a moderate background in elementary number theory and abstract algebra, Quadratic Number Fields offers an engaging first course in algebraic number theory, suitable for upper undergraduate students.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

348

Publisher

Springer Nature

Published Date

ISBN 10

3030786528

ISBN 13

9783030786526

Book's by Franz Halter-Koch

Class Field Theory and L Functions

Class Field Theory and L Functions

Quadratic Irrationals

Quadratic Irrationals

Ideal Systems

Ideal Systems

An Invitation To Algebraic Numbers And Algebraic Functions

An Invitation To Algebraic Numbers And Algebraic Functions

Non-Unique Factorizations

Non-Unique Factorizations

Class Field Theory and L Functions

Class Field Theory and L Functions

Reciprocity Laws

Reciprocity Laws

An Invitation To Algebraic Numbers And Algebraic Functions

An Invitation To Algebraic Numbers And Algebraic Functions

Quadratic Irrationals

Quadratic Irrationals

Quadratic Number Fields

Quadratic Number Fields

Username

Password

Username

Password

Password again

Birthday

Email