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              Books by Franz Halter-Koch

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              Quadratic Irrationals: An Introduction to Classical Number Theory
               

              Quadratic Irrationals: An Introduction to Classical Number Theory (Hardback)

              By Halter-Koch, Franz

              • RRP: $247.00
              • $247.00
              • To Order

              This work focuses on the number theory of quadratic irrationalities in various forms, including continued fractions, orders in quadratic number fields, and binary quadratic forms. It presents classical results obtained by the famous number theorists Gauss, Legendre, Lagrange, and... Dirichlet. Collecting information previously scattered in the literature, the book covers the classical theory of continued fractions, quadratic orders, binary quadratic forms, and class groups based on the concept of a quadratic irrational.
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              ISBN 9781466591837
              Released NZ 17 Jun 2013
              Publisher Taylor & Francis Inc
              Interest Age 19+ years
              Series Chapman & Hall/CRC Pure and Applied Mathematics
              Availability
              Indent title (internationally sourced), usually ships 4-6 weeks
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              Non-Unique Factorizations: Algebraic, Combinatorial and Analytic Theory

              Non-Unique Factorizations: Algebraic, Combinatorial and Analytic Theory (Hardback, Contains 278 Hardbacks)

              By Geroldinger, Alfred; Halter-Koch, Franz

              • RRP: $353.00
              • $353.00
              • In Stock At Publisher

              Presents the knowledge on the theory of non-unique factorizations and discusses its algebraic, combinatorial, and analytic fundamentals. This book focuses on factorization properties in rings of integers, orders of algebraic number fields, holomorphy rings, Krull and Mori domains..., Krull monoids, congruence monoids, and Hilbert monoids.
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              ISBN 9781584885764
              Released NZ 13 Jan 2006
              Publisher Taylor & Francis Inc
              Interest Age General Audience
              Series Chapman & Hall/CRC Pure and Applied Mathematics
              Availability
              In stock at publisher; ships 6-12 working days
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              An Invitation to Algebraic Numbers and Algebraic Functions

              An Invitation to Algebraic Numbers and Algebraic Functions (Hardback)

              By Halter-Koch, Franz

              • RRP: $235.00
              • $235.00
              • Delayed Release

              Through a set of related yet distinct texts, the author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions: Ideal- and valuation-theoretic aspects, L functions and class field theory, together with a presentation of algebraic found...ations which are usually undersized in standard algebra courses. These books contain the whole classical theory of algebraic numbers and algebraic functions together with the prerequists that too often receive short coverage in standard courses. Thus it should enable a broader audience to get acquainted with these theories.
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              ISBN 9781138583580
              Released NZ 15 Jan 2020
              Publisher Taylor & Francis Ltd
              Interest Age 19+ years
              Availability
              Pre-order title, release date has been delayed
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              An Invitation To Algebraic Numbers And Algebraic Functions
               

              An Invitation To Algebraic Numbers And Algebraic Functions (Hardback)

              By Halter-Koch, Franz

              • RRP: $235.00
              • $235.00
              • To Order

              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 differents, 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 it 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 the wealth of presented advanced topics the text is easily readable.
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              ISBN 9781138583610
              Released NZ 8 Jun 2020
              Publisher Taylor & Francis Ltd
              Interest Age 19+ years
              Availability
              Indent title (internationally sourced), usually ships 4-6 weeks
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              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 (Hardback, Reprint 2011)

              Edited by Halter-Koch, Franz; Tichy, Robert F.

              • RRP: $1,180.50
              • $993.61
              • Save $186.89
              • In Stock US

              Most of the 35 papers presented at the September 1998 conference discuss algebraic number theory, diophantine and algorithmic problems, diophantine equations, uniform distribution, and discrepancy theory. Topics include small values of diagonal cubic forms, galois module structur...e for wild extensions, the class number one problem for the dihedral C
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              ISBN 9783110163049
              Released NZ 17 May 2000
              Publisher De Gruyter
              Interest Age General Audience
              Series De Gruyter Proceedings in Mathematics
              Availability
              Internationally sourced; ships 6-12 working days
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