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2002
Gauss called the quadratic reciprocity law “the golden theorem.” He was the first to give a valid proof of this theorem. In fact, he found nine different proofs. After this he worked on biquadratic reciprocity, obtaining the correct statement, but not finding a proof. The first to do so were Eisenstein and Jacobi. The history of the general reciprocity
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Gauss called the quadratic reciprocity law “the golden theorem.” He was the first to give a valid proof of this theorem. In fact, he found nine different proofs. After this he worked on biquadratic reciprocity, obtaining the correct statement, but not finding a proof. The first to do so were Eisenstein and Jacobi. The history of the general reciprocity
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2000
Rational reciprocity deals with residue symbols which assume only the values ±1 and which have entries in ℤ; the first rational reciprocity laws other than quadratic reciprocity were discovered by Dirichlet. His results, however, were soon forgotten and have been rediscovered regularly.
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Rational reciprocity deals with residue symbols which assume only the values ±1 and which have entries in ℤ; the first rational reciprocity laws other than quadratic reciprocity were discovered by Dirichlet. His results, however, were soon forgotten and have been rediscovered regularly.
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1978
Iwasawa [Iw 8] proved general explicit reciprocity laws extending the classical results of Artin-Hasse, for applications to the study of units in cyclotomic fields. These were extended by Coates-Wiles [CW 1] and Wiles [Wi] to arbitrary Lubin-Tate groups.
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Iwasawa [Iw 8] proved general explicit reciprocity laws extending the classical results of Artin-Hasse, for applications to the study of units in cyclotomic fields. These were extended by Coates-Wiles [CW 1] and Wiles [Wi] to arbitrary Lubin-Tate groups.
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The Law of Quadratic Reciprocity
The Mathematical Gazette, 1938It is only after considerable hesitation that I have allowed myself to be persuaded to publish this paper, for it contains nothing whatever that cannot be obtained from any of the standard text-books on the Theory of Numbers. I have, however, been influenced by the fact that to many school-masters such text-books are not easy of ...
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2004
Since reciprocity laws play an important role in this book, we now describe several reciprocity laws appearing in number theory in terms of automorphism groups of a field fixing a given prime or a given point. Only this chapter contains (elementary) exercises.
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Since reciprocity laws play an important role in this book, we now describe several reciprocity laws appearing in number theory in terms of automorphism groups of a field fixing a given prime or a given point. Only this chapter contains (elementary) exercises.
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1987
Let F be the modular function field, studied in Chapter 6. We saw that F can be identified with the field of x-coordinates (or h-coordinates, h = Weber function) of division points of an elliptic curve A defined over Q(j), having invariant j.
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Let F be the modular function field, studied in Chapter 6. We saw that F can be identified with the field of x-coordinates (or h-coordinates, h = Weber function) of division points of an elliptic curve A defined over Q(j), having invariant j.
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An Explicit Reciprocity Law Associated to Some Finite Coverings of Algebraic Curves
, 2018J. M. Porras, F. P. Romo, F. J. Martín
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The Quadratic Reciprocity Law: A Collection of Classical Proofs
, 2015O. Baumgart, F. Lemmermeyer
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