Read An Invitation To Algebraic Numbers And Algebraic Functions

An Invitation To Algebraic Numbers And Algebraic Functions

Franz Halter-Koch

4.9/5 (10356 ratings)

Description: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).We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with An Invitation To Algebraic Numbers And Algebraic Functions. To get started finding An Invitation To Algebraic Numbers And Algebraic Functions, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

Pages: 595

Format: PDF, EPUB & Kindle Edition

Publisher: CRC Press

Release: 2020

ISBN: xnuJ

Description: 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).We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with An Invitation To Algebraic Numbers And Algebraic Functions. To get started finding An Invitation To Algebraic Numbers And Algebraic Functions, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

Special Offer | $0.00

Special Offer! | $0.00

An Invitation To Algebraic Numbers And Algebraic Functions

An Invitation To Algebraic Numbers And Algebraic Functions

More Books

Quadratic Irrationals: An Introduction to Classical Number Theory

Quadratic Irrationals: An Introduction to Classical Number Theory

Ideal Systems: An Introduction to Multiplicative Ideal Theory (Chapman & Hall/CRC Pure and Applied Mathematics) [4/21/1998] Franz Halter-Koch

Ideal Systems: An Introduction to Multiplicative Ideal Theory (Chapman & Hall/CRC Pure and Applied Mathematics) [4/21/1998] Franz Halter-Koch

Ideal Systems: An Introduction to Multiplicative Ideal Theory (Chapman & Hall/CRC Pure and Applied Mathematics)

Ideal Systems: An Introduction to Multiplicative Ideal Theory (Chapman & Hall/CRC Pure and Applied Mathematics)

Class Field Theory and L Functions: Foundations and Main Results

Class Field Theory and L Functions: Foundations and Main Results

Algebraic Number Theory and Diophantine Analysis: Proceedings of the International Conference Held in Graz, Austria, August 30 to September 5, 1998

Algebraic Number Theory and Diophantine Analysis: Proceedings of the International Conference Held in Graz, Austria, August 30 to September 5, 1998

Quadratic Irrationals

Quadratic Irrationals

Ideal Theory of Commutative Rings and Monoids (Lecture Notes in Mathematics)

Ideal Theory of Commutative Rings and Monoids (Lecture Notes in Mathematics)