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Reciprocity laws : from Euler to Eisenstein / Franz Lemmermeyer.

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Author/Creator:
Lemmermeyer, Franz, 1962-
Language:
English.
Publication date:
2000
Imprint:
Berlin ; New York : Springer, c2000.
Format:
  • Book
  • xix, 487 p. ; 24 cm.
Bibliography:
Includes bibliographical references and indexes.
Contents:
  • 1. The Genesis of Quadratic Reciprocity
  • 2. Quadratic Number Fields
  • 3. Cyclotomic Number Fields
  • 4. Power Residues and Gauss Sums
  • 5. Rational Reciprocity Laws
  • 6. Quartic Reciprocity
  • 7. Cubic Reciprocity
  • 8. Eisenstein's Analytic Proofs
  • 9. Octic Reciprocity
  • 10. Gauss's Last Entry
  • 11. Eisenstein Reciprocity.
Summary:
"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."--BOOK JACKET.
Series:
Springer monographs in mathematics, 1439-7382
Springer monographs in mathematics.
Subjects:
ISBN:
3540669574
9783540669579
3642086284
9783642086281

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