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Titlebook: Reciprocity Laws; From Euler to Eisens Franz Lemmermeyer Book 2000 Springer-Verlag Berlin Heidelberg 2000 Algebra.Elliptic functions.Gaus a

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书目名称Reciprocity Laws
副标题From Euler to Eisens
编辑Franz Lemmermeyer
视频video
丛书名称Springer Monographs in Mathematics
图书封面Titlebook: Reciprocity Laws; From Euler to Eisens Franz Lemmermeyer Book 2000 Springer-Verlag Berlin Heidelberg 2000 Algebra.Elliptic functions.Gaus a
描述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.
出版日期Book 2000
关键词Algebra; Elliptic functions; Gaus and Jacobi sums; Reciprocity Laws; Strickelberg‘s Theorem; Zeta functio
版次1
doihttps://doi.org/10.1007/978-3-662-12893-0
isbn_softcover978-3-642-08628-1
isbn_ebook978-3-662-12893-0Series ISSN 1439-7382 Series E-ISSN 2196-9922
issn_series 1439-7382
copyrightSpringer-Verlag Berlin Heidelberg 2000
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Reciprocity Laws978-3-662-12893-0Series ISSN 1439-7382 Series E-ISSN 2196-9922
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Cyclotomic Number Fields,This chapter is devoted to some proofs of the quadratic reciprocity law that make use of the arithmetic of cyclotomic number fields.
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Quartic Reciprocity,In Chapter 5 we have already seen a lot about quartic reciprocity and its applications to rational number theory; these rational laws, however, do not suffice to solve every “rational” problem where quartic reciprocity is involved, as the following example shows.
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,Gauss’s Last Entry,It is well known that Gauss recorded many of his discoveries in a diary; it ends with the ‘Last Entry’ from July 9, 1814, which reads as follows. (see [Kle]):
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The Genesis of Quadratic Reciprocity,und very early on (see [Ene]) — in connection with the problem of characterizing perfect squares — the history of modern number theory starts with the editions of the books of Diophantus, in particular with the commented edition by Bachet in 1621.
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