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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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 Eisensteins 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.
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In this first chapter we will present the fathers of the quadratic reciprocity law. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
octic reciprocity law, quartic reciprocity law, ratic reciprocity law, second supplementary law, first supplementary law, rational quartic reciprocity, cubic residuacity, cubic reciprocity law, rational reciprocity laws, quartic character, des résidus quadratiques, power residue character, quartic residue symbol, quadratic units, prime ideal factorization, quartic subfield, residue character modulo, normal integral bases, quartic residuacity, storia sci, cyclotomic numbers, cyclotomic number fields, genus theory, réciprocité quadratique, ramified prime ideals Key Phrases - Capitalized Phrases (CAPs): (learn more)
Reine Angew, Additional References, Springer Verlag, Zur Theorie, Acta Arith, London Math, Crelle's Journal, New York, Kronecker's Jugendtraum, Pures Appl, Cambridge Phil, Cambridge Univ, Japan Acad, Nieuw Arch, Pure Math, Acta Math, Disquisitiones Arithmeticae, Duke Math, Exact Sci, Hensel's Lemma, Hilbert's Zahlbericht, Historia Math, Legendre's Lemma, Norske Vid, Sums of Gauss New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this first chapter we will present the fathers of the quadratic reciprocity law. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
octic reciprocity law, quartic reciprocity law, ratic reciprocity law, second supplementary law, first supplementary law, rational quartic reciprocity, cubic residuacity, cubic reciprocity law, rational reciprocity laws, quartic character, des résidus quadratiques, power residue character, quartic residue symbol, quadratic units, prime ideal factorization, quartic subfield, residue character modulo, normal integral bases, quartic residuacity, storia sci, cyclotomic numbers, cyclotomic number fields, genus theory, réciprocité quadratique, ramified prime ideals Key Phrases - Capitalized Phrases (CAPs): (learn more)
Reine Angew, Additional References, Springer Verlag, Zur Theorie, Acta Arith, London Math, Crelle's Journal, New York, Kronecker's Jugendtraum, Pures Appl, Cambridge Phil, Cambridge Univ, Japan Acad, Nieuw Arch, Pure Math, Acta Math, Disquisitiones Arithmeticae, Duke Math, Exact Sci, Hensel's Lemma, Hilbert's Zahlbericht, Historia Math, Legendre's Lemma, Norske Vid, Sums of Gauss New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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This book cites 32
books:
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23
books
cite this book:
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- Disquisitiones Arithmeticae by Carl F. Gauss on 7 pages
- Number Theory: An approach through history from Hammurapi to Legendre by André Weil on 6 pages
- Number Theory by Helmut Hasse on 6 pages
- Introduction to Cyclotomic Fields (Graduate Texts in Mathematics) by Lawrence C. Washington on 4 pages
- Arithmetic of Algebraic Curves (Monographs in Contemporary Mathematics) by Serguei A. Stepanov on page 41, page 109, and page 355
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- Valued Fields (Springer Monographs in Mathematics) by Antonio J. Engler in Back Matter
- Elementary and Analytic Theory of Algebraic Numbers (Springer Monographs in Mathematics) by Wladyslaw Narkiewicz in Back Matter
- Lie Algebras and Algebraic Groups (Springer Monographs in Mathematics) by Patrice Tauvel in Back Matter
- Nonstandard Analysis, Axiomatically (Springer Monographs in Mathematics) by Vladimir Kanovei in Back Matter
- Serre's Problem on Projective Modules by T.Y. Lam in Back Matter
See all 23 books citing this book
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