Franz Lemmermeyer's Books

The Hasse - Noether Correspondence 1925 -1935

English Translation with Extensive Commentary

By: Peter Roquette,Franz Lemmermeyer

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The Hasse - Noether Correspondence 1925 -1935

English Translation with Extensive Commentary

By: Peter Roquette,Franz Lemmermeyer

Providing the first comprehensive account of the widely unknown cooperation and friendship between Emmy Noether and Helmut Hasse, this book contains English translations of all available letters which were exchanged between them in the years 1925-1935. It features a special chapter on class field theory, a subject which was completely renewed in those years, Noether and Hasse being among its main proponents. These historical items give evidence that Emmy Noether's impact on the development of mathematics is not confined to abstract algebra but also extends to important ideas in modern class field theory as part of algebraic number theory. In her letters, details of proofs appear alongside conjectures and speculations, offering a rich source for those who are interested in the rise and development of mathematical notions and ideas. The letters are supplemented by extensive comments, helping the reader to understand their content within the mathematical environment of the 1920s and 1930s.

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Page Count

328

Publisher

Springer Nature

Published Date

ISBN 10

303112880X

ISBN 13

9783031128806

Quadratic Number Fields

By: Franz Lemmermeyer

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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.

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348

Publisher

Springer Nature

Published Date

ISBN 10

3030786528

ISBN 13

9783030786526

Reciprocity Laws

From Euler to Eisenstein

By: Franz Lemmermeyer

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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.

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503

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662128934

ISBN 13

9783662128930

Rational Algebraic Curves

A Computer Algebra Approach

By: J. Rafael Sendra,Franz Winkler,Sonia Pérez-Diaz

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Rational Algebraic Curves

A Computer Algebra Approach

By: J. Rafael Sendra,Franz Winkler,Sonia Pérez-Diaz

The central problem considered in this introduction for graduate students is the determination of rational parametrizability of an algebraic curve and, in the positive case, the computation of a good rational parametrization. This amounts to determining the genus of a curve: its complete singularity structure, computing regular points of the curve in small coordinate fields, and constructing linear systems of curves with prescribed intersection multiplicities. The book discusses various optimality criteria for rational parametrizations of algebraic curves.

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273

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Springer Science & Business Media

Published Date

ISBN 10

3540737251

ISBN 13

9783540737254

An Invitation To Algebraic Numbers And Algebraic Functions

By: Franz Halter-Koch

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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).

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595

Publisher

CRC Press

Published Date

ISBN 10

0429014678

ISBN 13

9780429014673

Quadratic Irrationals

An Introduction to Classical Number Theory

By: Franz Halter-Koch

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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

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Page Count

431

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CRC Press

Published Date

ISBN 10

1466591846

ISBN 13

9781466591844

Quadratic Number Fields

By: Franz Lemmermeyer

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Quadratic Number Fields

By: Franz Lemmermeyer

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Page Count

348

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Springer Nature

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ISBN 10

3030786528

ISBN 13

9783030786526

The Hasse - Noether Correspondence 1925 -1935

English Translation with Extensive Commentary

By: Peter Roquette,Franz Lemmermeyer

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The Hasse - Noether Correspondence 1925 -1935

English Translation with Extensive Commentary

By: Peter Roquette,Franz Lemmermeyer

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Solve jigsaw puzzle

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Page Count

328

Publisher

Springer Nature

Published Date

ISBN 10

303112880X

ISBN 13

9783031128806

Reciprocity Laws

From Euler to Eisenstein

By: Franz Lemmermeyer

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Reciprocity Laws

From Euler to Eisenstein

By: Franz Lemmermeyer

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Solve jigsaw puzzle

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Page Count

503

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662128934

ISBN 13

9783662128930

Book's by Franz Lemmermeyer

The Hasse - Noether Correspondence 1925 -1935

The Hasse - Noether Correspondence 1925 -1935

Quadratic Number Fields

Quadratic Number Fields

Reciprocity Laws

Reciprocity Laws

Rational Algebraic Curves

Rational Algebraic Curves

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

The Hasse - Noether Correspondence 1925 -1935

The Hasse - Noether Correspondence 1925 -1935

Reciprocity Laws

Reciprocity Laws

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