Lemmermeyer, Franz 1962
Overview
Works:  37 works in 117 publications in 2 languages and 1,549 library holdings 

Genres:  Records and correspondence History Textbooks 
Roles:  Editor, Author, Translator, Creator 
Classifications:  QA247, 512.74 
Publication Timeline
.
Most widely held works by
Franz Lemmermeyer
Reciprocity laws : from Euler to Eisenstein by
Franz Lemmermeyer(
Book
)
14 editions published between 2000 and 2010 in English and held by 439 WorldCat member libraries worldwide
"This book is about 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 Eisenstein's reciprocity law. An extensive bibliography will particularly appeal to readers interested in the history of reciprocity laws or in the current research in this area."Jacket
14 editions published between 2000 and 2010 in English and held by 439 WorldCat member libraries worldwide
"This book is about 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 Eisenstein's reciprocity law. An extensive bibliography will particularly appeal to readers interested in the history of reciprocity laws or in the current research in this area."Jacket
Helmut Hasse und Emmy Noether : die Korrespondenz 19251935 by
Helmut Hasse(
Book
)
12 editions published in 2006 in 3 languages and held by 80 WorldCat member libraries worldwide
This book reproduces the complete extant correspondence between Emmy Noether and Helmut Hasse. There are 82 such letters, of which 79 are from Noether to Hasse, dating from 1925 until Noethers sudden death in 1935. The correspondence refl ects a crucial period in the development of 20th century algebra and number theory, in particular class fi eld theory. Details of proofs appear alongside with conjectures and speculations. Also discussed are questions of textbook presentation, e.g., of Galois theory. Aside from mathematical details, the spontaneity of Noethers style allows many glimpses at the image that Emmy Noether and Helmut Hasse had of the topics they were working in. The Hasse Noether correspondence is a rich source for those who are interested in the rise and the development of mathematical notions and ideas. Each letter is accompanied by a detailed commentary supplied by the editors. For the convenience of the reader, numerous crossreferences, extended indexes, and short biographies of all persons mentioned in the correspondence have been added
12 editions published in 2006 in 3 languages and held by 80 WorldCat member libraries worldwide
This book reproduces the complete extant correspondence between Emmy Noether and Helmut Hasse. There are 82 such letters, of which 79 are from Noether to Hasse, dating from 1925 until Noethers sudden death in 1935. The correspondence refl ects a crucial period in the development of 20th century algebra and number theory, in particular class fi eld theory. Details of proofs appear alongside with conjectures and speculations. Also discussed are questions of textbook presentation, e.g., of Galois theory. Aside from mathematical details, the spontaneity of Noethers style allows many glimpses at the image that Emmy Noether and Helmut Hasse had of the topics they were working in. The Hasse Noether correspondence is a rich source for those who are interested in the rise and the development of mathematical notions and ideas. Each letter is accompanied by a detailed commentary supplied by the editors. For the convenience of the reader, numerous crossreferences, extended indexes, and short biographies of all persons mentioned in the correspondence have been added
Emil Artin and Helmut Hasse : the correspondence 19231958 by
Emil Artin(
Book
)
23 editions published between 2008 and 2014 in English and German and held by 54 WorldCat member libraries worldwide
This volume presents English translations of the letters exchanged between Emil Artin and Helmut Hasse written from 1921 to 1958. The letters are accompanied by extensive comments explaining the mathematical background and providing other essential context. Most letters deal with class field theory and shed new light on the birth of one of its most profound results: Artin's reciprocity law
23 editions published between 2008 and 2014 in English and German and held by 54 WorldCat member libraries worldwide
This volume presents English translations of the letters exchanged between Emil Artin and Helmut Hasse written from 1921 to 1958. The letters are accompanied by extensive comments explaining the mathematical background and providing other essential context. Most letters deal with class field theory and shed new light on the birth of one of its most profound results: Artin's reciprocity law
Vorlesungen über Zahlentheorie : Carl Gustav Jacob Jacobi ; Wintersemester 1836/37, Königsberg by
C. G. J Jacobi(
Book
)
5 editions published between 2006 and 2007 in German and English and held by 42 WorldCat member libraries worldwide
5 editions published between 2006 and 2007 in German and English and held by 42 WorldCat member libraries worldwide
Algebra by
Falko Lorenz(
Book
)
2 editions published in 2007 in German and held by 29 WorldCat member libraries worldwide
Introduces the reader to the classical parts of algebra. This book ends with an appendix containing exercises and notes on the previous parts of the book. Brief historical comments and suggestions for further reading are also scattered through the text
2 editions published in 2007 in German and held by 29 WorldCat member libraries worldwide
Introduces the reader to the classical parts of algebra. This book ends with an appendix containing exercises and notes on the previous parts of the book. Brief historical comments and suggestions for further reading are also scattered through the text
Emil Artin und Helmut Hasse by
Peter Roquette(
)
1 edition published in 2008 in German and held by 20 WorldCat member libraries worldwide
1 edition published in 2008 in German and held by 20 WorldCat member libraries worldwide
Helmut Hasse und Emmy Noether ; die Korrespondenz 1925  1935 by
Peter Roquette(
)
2 editions published in 2006 in Undetermined and held by 20 WorldCat member libraries worldwide
2 editions published in 2006 in Undetermined and held by 20 WorldCat member libraries worldwide
Die mathematischen Tagebücher von Helmut Hasse 19231935 by
Franz Lemmermeyer(
)
1 edition published in 2012 in German and held by 20 WorldCat member libraries worldwide
1 edition published in 2012 in German and held by 20 WorldCat member libraries worldwide
Körper und Galoistheorie by
Falko Lorenz(
Book
)
1 edition published in 2007 in German and held by 19 WorldCat member libraries worldwide
1 edition published in 2007 in German and held by 19 WorldCat member libraries worldwide
Mathematik à la Carte : Elementargeometrie an Quadratwurzeln mit einigen geschichtlichen Bemerkungen by
Franz Lemmermeyer(
Book
)
4 editions published between 2014 and 2015 in German and held by 17 WorldCat member libraries worldwide
4 editions published between 2014 and 2015 in German and held by 17 WorldCat member libraries worldwide
The quadratic reciprocity law : a collection of classical proofs by
Oswald Baumgart(
Book
)
3 editions published in 2015 in English and held by 17 WorldCat member libraries worldwide
This book is the English translation of Baumgart's thesis on the early proofs of the quadratic reciprocity law (Über das quadratische Reciprocitätsgesetz. Eine vergleichende Darstellung der Beweise), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre, as well as detailed descriptions of several early proofs of the quadratic reciprocity law. The second part highlights Baumgart's comparisons of the principles behind these proofs. A current list of all known proofs of the quadratic reciprocity law, with complete references, is provided in the appendix. This book will appeal to all readers interested in elementary number theory and the history of number theory
3 editions published in 2015 in English and held by 17 WorldCat member libraries worldwide
This book is the English translation of Baumgart's thesis on the early proofs of the quadratic reciprocity law (Über das quadratische Reciprocitätsgesetz. Eine vergleichende Darstellung der Beweise), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre, as well as detailed descriptions of several early proofs of the quadratic reciprocity law. The second part highlights Baumgart's comparisons of the principles behind these proofs. A current list of all known proofs of the quadratic reciprocity law, with complete references, is provided in the appendix. This book will appeal to all readers interested in elementary number theory and the history of number theory
Correspondence of Leonhard Euler with Christian Goldbach by
Leonhard Euler(
Book
)
8 editions published in 2015 in English and held by 17 WorldCat member libraries worldwide
8 editions published in 2015 in English and held by 17 WorldCat member libraries worldwide
Galois theory of pextensions by
Helmut Koch(
Book
)
2 editions published between 2002 and 2011 in English and held by 16 WorldCat member libraries worldwide
First published in German in 1970 and translated into Russian in 1973, this classic now becomes available in English. After introducing the theory of prop groups and their cohomology, it discusses presentations of the Galois groups G S of maximal pextensions of number fields that are unramified outside a given set S of primes. It computes generators and relations as well as the cohomological dimension of some G S, and gives applications to infinite class field towers. The book demonstrates that the cohomology of groups is very useful for studying Galois theory of number fields; at the same time, it offers a down to earth introduction to the cohomological method. In a "Postscript" Helmut Koch and Franz Lemmermeyer give a survey on the development of the field in the last 30 years. Also, a list of additional, recent references has been included
2 editions published between 2002 and 2011 in English and held by 16 WorldCat member libraries worldwide
First published in German in 1970 and translated into Russian in 1973, this classic now becomes available in English. After introducing the theory of prop groups and their cohomology, it discusses presentations of the Galois groups G S of maximal pextensions of number fields that are unramified outside a given set S of primes. It computes generators and relations as well as the cohomological dimension of some G S, and gives applications to infinite class field towers. The book demonstrates that the cohomology of groups is very useful for studying Galois theory of number fields; at the same time, it offers a down to earth introduction to the cohomological method. In a "Postscript" Helmut Koch and Franz Lemmermeyer give a survey on the development of the field in the last 30 years. Also, a list of additional, recent references has been included
The theory of algebraic number fields by
David Hilbert(
Book
)
3 editions published in 1998 in English and held by 14 WorldCat member libraries worldwide
This book is an English translation of Hilbert's Zahlbericht, the monumental report on the theory of algebraic number field which he composed for the German Mathematical Society. In this magisterial work Hilbert provides a unified account of the development of algebraic number theory up to the end of the nineteenth century. He greatly simplified Kummer's theory and laid the foundation for a general theory of abelian fields and class field theory. David Hilbert (18621943) made great contributions to many areas of mathematics  invariant theory, algebraic number theory, the foundations of geometry, integral equations, the foundations of mathematics and mathematical physics. He is remembered also for his lecture at the Paris International Congress of Mathematicians in 1900 where he presented a set of 23 problems "from the discussion of which an advancement of science may be expected"His expectations have been amply fulfilled
3 editions published in 1998 in English and held by 14 WorldCat member libraries worldwide
This book is an English translation of Hilbert's Zahlbericht, the monumental report on the theory of algebraic number field which he composed for the German Mathematical Society. In this magisterial work Hilbert provides a unified account of the development of algebraic number theory up to the end of the nineteenth century. He greatly simplified Kummer's theory and laid the foundation for a general theory of abelian fields and class field theory. David Hilbert (18621943) made great contributions to many areas of mathematics  invariant theory, algebraic number theory, the foundations of geometry, integral equations, the foundations of mathematics and mathematical physics. He is remembered also for his lecture at the Paris International Congress of Mathematicians in 1900 where he presented a set of 23 problems "from the discussion of which an advancement of science may be expected"His expectations have been amply fulfilled
Class field theory : the Bonn Lectures by
Jürgen Neukirch(
Book
)
3 editions published in 2013 in English and held by 9 WorldCat member libraries worldwide
The present manuscript is an improved edition of a text that first appeared under the same title in Bonner Mathematische Schriften, no.26, and originated from a series of lectures given by the author in 1965/66 in Wolfgang Krull's seminar in Bonn. Its main goal is to provide the reader, acquainted with the basics of algebraic number theory, a quick and immediate access to class field theory. This script consists of three parts, the first of which discusses the cohomology of finite groups. The second part discusses local class field theory, and the third part concerns the class field theory of finite algebraic number fields
3 editions published in 2013 in English and held by 9 WorldCat member libraries worldwide
The present manuscript is an improved edition of a text that first appeared under the same title in Bonner Mathematische Schriften, no.26, and originated from a series of lectures given by the author in 1965/66 in Wolfgang Krull's seminar in Bonn. Its main goal is to provide the reader, acquainted with the basics of algebraic number theory, a quick and immediate access to class field theory. This script consists of three parts, the first of which discusses the cohomology of finite groups. The second part discusses local class field theory, and the third part concerns the class field theory of finite algebraic number fields
Leonhardi Euleri Opera omnia by
Leonhard Euler(
Book
)
2 editions published in 2015 in English and held by 8 WorldCat member libraries worldwide
2 editions published in 2015 in English and held by 8 WorldCat member libraries worldwide
Opera omnia by
Leonhard Euler(
Book
)
2 editions published in 2015 in German and English and held by 8 WorldCat member libraries worldwide
2 editions published in 2015 in German and English and held by 8 WorldCat member libraries worldwide
Leonhardi Euleri Opera omnia by
Leonhard Euler(
Book
)
2 editions published in 2015 in German and held by 8 WorldCat member libraries worldwide
2 editions published in 2015 in German and held by 8 WorldCat member libraries worldwide
Emil Artin und Helmut Hasse die Korrespondenz 19231934 = Emil Artin and Helmut Hasse : their correspondence 1923 1934(
)
1 edition published in 2008 in German and held by 6 WorldCat member libraries worldwide
This book contains the full text of the letters from Emil Artin to Helmut Hasse, as they are preserved in the Handschriftenabteilung of the Göttingen University Library. There are 49 such letters, written in the years 19231934, discussing mathematical problems of the time. The corresponding letters in the other direction, i.e., from Hasse to Artin, seem to be lost. We have supplemented Artin's letters by detailed comments, combined with a description of the mathematical environment of Hasse and Artin, and of the relevant literature. In this way it has become possible to sufficiently reconstruct the content of the corresponding letters from Hasse to Artin too. Artin and Hasse were among those who shaped modern algebraic number theory, in particular class field theory. Their correspondence admits a view of the ideas which led to the great achievements of their time, starting from Artin's Lseries and his reciprocity law towards Hasse's norm symbol, local class field theory and the LocalGlobal Principle. These letters are a valuable source for understanding the rise and development of mathematical ideas and notions as we see them today. The book is a followup of our earlier book on the correspondence between Hasse and Emmy Noether. It is thus the second of a series which aims to open access to the rich collection of Hasse's mathematical letters and notes contained in the Göttingen Handschriftenabteilung
1 edition published in 2008 in German and held by 6 WorldCat member libraries worldwide
This book contains the full text of the letters from Emil Artin to Helmut Hasse, as they are preserved in the Handschriftenabteilung of the Göttingen University Library. There are 49 such letters, written in the years 19231934, discussing mathematical problems of the time. The corresponding letters in the other direction, i.e., from Hasse to Artin, seem to be lost. We have supplemented Artin's letters by detailed comments, combined with a description of the mathematical environment of Hasse and Artin, and of the relevant literature. In this way it has become possible to sufficiently reconstruct the content of the corresponding letters from Hasse to Artin too. Artin and Hasse were among those who shaped modern algebraic number theory, in particular class field theory. Their correspondence admits a view of the ideas which led to the great achievements of their time, starting from Artin's Lseries and his reciprocity law towards Hasse's norm symbol, local class field theory and the LocalGlobal Principle. These letters are a valuable source for understanding the rise and development of mathematical ideas and notions as we see them today. The book is a followup of our earlier book on the correspondence between Hasse and Emmy Noether. It is thus the second of a series which aims to open access to the rich collection of Hasse's mathematical letters and notes contained in the Göttingen Handschriftenabteilung
Die mathematischen Tagebücher von Helmut Hasse 1923  1935 with an introduction in English(
)
1 edition published in 2012 in German and held by 6 WorldCat member libraries worldwide
This book contains the full text of the mathematical notebooks of Helmut Hasse (18981979), who was one of the leading mathematicians of the 20th century. The originals have been preserved in the Handschriftenabteilung at the Göttingen University Library. There are a total of seven volumes which contain 98 entries all together; these span the time period from July 1923 to February 1935. Each of the entries is preceded by a short comment. An extensive bibliography is provided.Compared to the other documents and papers from Hasse Nachlass at Göttingen, these papers are quite different. They detail Hasse's mathematical background, interests and his way of approaching problems. Many of the entries are inspired by Hasse's discussions with other mathematicians (for example, Emil Artin is often mentioned).One of the notable highlights in the entries is the first documentation of Artin's conjecture on primitive roots (1927), which Hasse noted down after a discussion with Artin. Another example is the first proof of the Riemann hypothesis for an extended class of function fields of high genus, namely those of the generalised Fermat fields with a finite field of constants (1932), after corresponding with Harold Davenport
1 edition published in 2012 in German and held by 6 WorldCat member libraries worldwide
This book contains the full text of the mathematical notebooks of Helmut Hasse (18981979), who was one of the leading mathematicians of the 20th century. The originals have been preserved in the Handschriftenabteilung at the Göttingen University Library. There are a total of seven volumes which contain 98 entries all together; these span the time period from July 1923 to February 1935. Each of the entries is preceded by a short comment. An extensive bibliography is provided.Compared to the other documents and papers from Hasse Nachlass at Göttingen, these papers are quite different. They detail Hasse's mathematical background, interests and his way of approaching problems. Many of the entries are inspired by Hasse's discussions with other mathematicians (for example, Emil Artin is often mentioned).One of the notable highlights in the entries is the first documentation of Artin's conjecture on primitive roots (1927), which Hasse noted down after a discussion with Artin. Another example is the first proof of the Riemann hypothesis for an extended class of function fields of high genus, namely those of the generalised Fermat fields with a finite field of constants (1932), after corresponding with Harold Davenport
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Related Identities
 Roquette, Peter 1927 Author Editor Creator
 Hasse, Helmut 18981979 Honoree Author
 Frei, Günther Author Editor Creator
 Artin, Emil 18981962 Author
 Baumgart, Oswald Author
 Noether, Emmy 18821935 Honoree
 Lorenz, Falko Author
 Euler, Leonhard 17071783 Correspondent Author
 Jacobi, Carl Gustav Jacob Author
 Goldbach, Christian 16901764 Correspondent
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Alternative Names
Franz Lemmermeyer deutscher Mathematiker
Franz Lemmermeyer Duits wiskundige
Franz Lemmermeyer escritor de no ficción y matemático aleman
Franz Lemmermeyer German mathematician and historian of mathematics
Lemmermeyer, F.
Lemmermeyer, Franz Josef 1962
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