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17 produkter

Invitation To Algebraic Numbers And Algebraic Functions
AvFranz Halter-Koch
E-bok
Engelska, 2020
1 224 kr
Läs direkt efter köp
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).
Invitation To Algebraic Numbers And Algebraic Functions
AvFranz Halter-Koch
E-bok
PDF, Engelska, 2020
1 237 kr
Läs direkt efter köp
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).
Class Field Theory and L Functions
Foundations and Main Results
AvFranz Halter-Koch
E-bok
Engelska, 2022
1 305 kr
Läs direkt efter köp
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.
Class Field Theory and L Functions
Foundations and Main Results
AvFranz Halter-Koch
E-bok
PDF, Engelska, 2022
1 291 kr
Läs direkt efter köp
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.
Class Field Theory and L Functions
Foundations and Main Results
AvFranz Halter-Koch
Häftad, Engelska, 2024
1 103 kr
Skickas inom 10-15 vardagar
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.
Invitation To Algebraic Numbers And Algebraic Functions
AvFranz Halter-Koch
Häftad, Engelska, 2024
1 046 kr
Skickas inom 10-15 vardagar
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).
Quadratic Irrationals
An Introduction to Classical Number Theory
AvFranz Halter-Koch
Häftad, Engelska, 2024
889 kr
Skickas inom 10-15 vardagar
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.The book highlights the connection between Gauss’s theory of binary forms and the arithmetic of quadratic orders. It collects essential results of the theory that have previously been difficult to access and scattered in the literature, including binary quadratic Diophantine equations and explicit continued fractions, biquadratic class group characters, the divisibility of class numbers by 16, F. Mertens’ proof of Gauss’s duplication theorem, and a theory of binary quadratic forms that departs from the restriction to fundamental discriminants. The book also proves Dirichlet’s theorem on primes in arithmetic progressions, covers Dirichlet’s class number formula, and shows that every primitive binary quadratic form represents infinitely many primes. The necessary fundamentals on algebra and elementary number theory are given in an appendix.Research on number theory has produced a wealth of interesting and beautiful results yet topics are strewn throughout the literature, the notation is far from being standardized, and a unifying approach to the different aspects is lacking. Covering both classical and recent results, this book unifies the theory of continued fractions, quadratic orders, binary quadratic forms, and class groups based on the concept of a quadratic irrational.
Non-Unique Factorizations
Algebraic, Combinatorial and Analytic Theory
AvFranz Halter-Koch,Alfred Geroldinger
E-bok
Engelska, 2006
3 558 kr
Läs direkt efter köp
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
Quadratic Irrationals
An Introduction to Classical Number Theory
AvFranz Halter-Koch
E-bok
Engelska, 2013
1 040 kr
Läs direkt efter köp
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
Class Field Theory and L Functions
Foundations and Main Results
AvFranz Halter-Koch
Inbunden, Engelska, 2022
2 085 kr
Skickas inom 10-15 vardagar
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.
Invitation To Algebraic Numbers And Algebraic Functions
AvFranz Halter-Koch
Inbunden, Engelska, 2020
2 085 kr
Skickas inom 10-15 vardagar
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).
Non-Unique Factorizations
Algebraic, Combinatorial and Analytic Theory
AvFranz Halter-Koch,Alfred Geroldinger
E-bok
PDF, Engelska, 2006
3 558 kr
Läs direkt efter köp
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
Quadratic Irrationals
An Introduction to Classical Number Theory
AvFranz Halter-Koch
Inbunden, Engelska, 2013
2 995 kr
Skickas inom 10-15 vardagar
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.The book highlights the connection between Gauss’s theory of binary forms and the arithmetic of quadratic orders. It collects essential results of the theory that have previously been difficult to access and scattered in the literature, including binary quadratic Diophantine equations and explicit continued fractions, biquadratic class group characters, the divisibility of class numbers by 16, F. Mertens’ proof of Gauss’s duplication theorem, and a theory of binary quadratic forms that departs from the restriction to fundamental discriminants. The book also proves Dirichlet’s theorem on primes in arithmetic progressions, covers Dirichlet’s class number formula, and shows that every primitive binary quadratic form represents infinitely many primes. The necessary fundamentals on algebra and elementary number theory are given in an appendix.Research on number theory has produced a wealth of interesting and beautiful results yet topics are strewn throughout the literature, the notation is far from being standardized, and a unifying approach to the different aspects is lacking. Covering both classical and recent results, this book unifies the theory of continued fractions, quadratic orders, binary quadratic forms, and class groups based on the concept of a quadratic irrational.
Quadratic Irrationals
An Introduction to Classical Number Theory
AvFranz Halter-Koch
E-bok
PDF, Engelska, 2013
1 040 kr
Läs direkt efter köp
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
Non-Unique Factorizations
Algebraic, Combinatorial and Analytic Theory
AvAlfred Geroldinger,Franz Halter-Koch
Inbunden, Engelska, 2006
2 995 kr
Skickas inom 10-15 vardagar
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 Factorizations: Algebraic, Combinatorial, and Analytic Theory offers a look at the present state of the theory in a single, unified resource.Taking a broad look at the algebraic, combinatorial, and analytic fundamentals, this book derives factorization results and applies them in concrete arithmetical situations using appropriate transfer principles. It begins with a basic introduction that can be understood with knowledge of standard basic algebra. The authors then move to the algebraic theory of monoids, arithmetic theory of monoids, the structure of sets of lengths, additive group theory, arithmetical invariants, and the arithmetic of Krull monoids. They also provide a self-contained introduction to abstract analytic number theory as well as a modern treatment of W. Narkiewicz's analytic theory of non-unique factorizations.Non-Unique Factorizations: Algebraic, Combinatorial, and Analytic Theory builds the discussion from first principles to applied problem solving, making it ideally suited to those not familiar with the theory as well as those who wish to deepen their understanding.
Del 2368 - Lecture Notes in Mathematics
Ideal Theory of Commutative Rings and Monoids
AvFranz Halter-Koch,Alfred Geroldingerm. fl.
Häftad, Engelska, 2025
833 kr
Skickas inom 10-15 vardagar
This book offers a concise treatment of multiplicative ideal theory in the language of multiplicative monoids. It presents a systematic development of the theory of weak ideal systems and weak module systems on arbitrary commutative monoids. Examples of monoids that are investigated include, but are not limited to, Mori monoids, Laskerian monoids, Prüfer monoids and Krull monoids. An in-depth study of various constructions from ring theory is also provided, with an emphasis on polynomial rings, Kronecker function rings and Nagata rings. The target audience is graduate students and researchers in ring and semigroup theory.
Ideal Theory of Commutative Rings and Monoids
AvFranz Halter-Koch,Andreas Reinhartm. fl.
E-bok
Engelska, 2025
1 026 kr
Läs direkt efter köp
This book offers a concise treatment of multiplicative ideal theory in the language of multiplicative monoids. It presents a systematic development of the theory of weak ideal systems and weak module systems on arbitrary commutative monoids. Examples of monoids that are investigated include, but are not limited to, Mori monoids, Laskerian monoids, Prüfer monoids and Krull monoids. An in-depth study of various constructions from ring theory is also provided, with an emphasis on polynomial rings, Kronecker function rings and Nagata rings. The target audience is graduate students and researchers in ring and semigroup theory.

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Franz Halter-Koch – författare

Invitation To Algebraic Numbers And Algebraic Functions

Invitation To Algebraic Numbers And Algebraic Functions

Class Field Theory and L Functions

Class Field Theory and L Functions

Class Field Theory and L Functions

Invitation To Algebraic Numbers And Algebraic Functions

Quadratic Irrationals

Non-Unique Factorizations

Quadratic Irrationals

Class Field Theory and L Functions

Invitation To Algebraic Numbers And Algebraic Functions

Non-Unique Factorizations

Quadratic Irrationals

Quadratic Irrationals

Non-Unique Factorizations

Ideal Theory of Commutative Rings and Monoids

Ideal Theory of Commutative Rings and Monoids

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Mina sidor

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Hjälp

Om Bokus

Om Bokus

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Inspiration

Inspiration