Reciprocity Laws

From Euler to Eisenstein

Franz Lemmermeyer (Autor)

Buch | Softcover

XX, 492 Seiten

2010
Springer Berlin (Verlag)
978-3-642-08628-1 (ISBN)

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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.

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.- A. Dramatis Personae.- B. Chronology of Proofs.- C. Some Open Problems.- References.- Author Index.

Erscheint lt. Verlag	3.12.2010
Reihe/Serie	Springer Monographs in Mathematics
Zusatzinfo	XX, 492 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	766 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Algebra • elliptic functions • Gaus and Jacobi sums • Number Theory • Reciprocity Laws • Strickelberg's Theorem • Zeta functions
ISBN-10	3-642-08628-4 / 3642086284
ISBN-13	978-3-642-08628-1 / 9783642086281
Zustand	Neuware