The Artin reciprocity law, which was established by Emil Artin in a series of papers (1924; 1927; 1930), is a general theorem in number theory that forms a central part of global class field theory.[1] The term "reciprocity law" refers to a long line of more concrete number theoretic statements which it generalized, from the quadratic reciprocity law and the reciprocity laws of Eisenstein and Kummer to Hilbert's product formula for the norm symbol. Artin's result provided a partial solution to Hilbert's ninth problem.
^Helmut Hasse, History of Class Field Theory, in Algebraic Number Theory, edited by Cassels and Frölich, Academic Press, 1967, pp. 266–279
The Artinreciprocity law, which was established by Emil Artin in a series of papers (1924; 1927; 1930), is a general theorem in number theory that forms...
the reciprocity laws as saying that a product over p of Hilbert norm residue symbols (a,b/p), taking values in roots of unity, is equal to 1. Artin reformulated...
solvable Artinreciprocity law, a general theorem in number theory that provided a partial solution to Hilbert's ninth problem Reciprocity relation or...
algebraic geometry, culminating in Artinreciprocity, class field theory, and the Langlands program. Quadratic reciprocity arises from certain subtle factorization...
the program may be seen as Emil Artin'sreciprocity law, which generalizes quadratic reciprocity. The Artinreciprocity law applies to a Galois extension...
Reciprocity theorem may refer to: Quadratic reciprocity, a theorem about modular arithmetic Cubic reciprocity Quartic reciprocityArtinreciprocity Weil...
statements of the Artinreciprocity law is that this results in a canonical isomorphism. Neukirch 1999, p. 134, Sec. 5. Artin & Whaples 1945. Artin & Whaples...
class group of F. This statement was generalized to the so called Artinreciprocity law; in the idelic language, writing CF for the idele class group...
simplest of the higher reciprocity laws, and is a consequence of several later and stronger reciprocity laws such as the Artinreciprocity law. It was introduced...
Emil Artin, a mathematician. Ankeny–Artin–Chowla congruence Artin algebra Artin billiards Artin braid group Artin character Artin conductor Artin's conjecture...
allows one to describe the Artinreciprocity law, which is a generalisation of quadratic reciprocity, and other reciprocity laws over finite fields. In...
mostly proved by 1930, after work by Teiji Takagi. Emil Artin established the Artinreciprocity law in a series of papers (1924; 1927; 1930). This law...
of reals or p-adic numbers. It is related to reciprocity laws, and can be defined in terms of the Artin symbol of local class field theory. The Hilbert...
quite a deep one, in the sense that it motivates some of the ideas of Artinreciprocity. Suppose that p is an odd prime. The action takes place inside the...
titled Basic Galois Theory. His ideas were used by Emil Artin to prove the Artinreciprocity law. He worked with his student Anatoly Dorodnov on a generalization...
vector spaces. Artin's study of these representations led him to formulate the Artinreciprocity law and conjecture what is now called the Artin conjecture...
symbol may refer to: The local Artin symbol in Artinreciprocity The local symbol used to formulate Weil reciprocity A Steinberg symbol on a local field...
certain finite invariants, mapping from the idele class group under the Artinreciprocity law. Herein, the analytical structure of its L-function allows for...
theorem Hilbert class field Takagi existence theorem Hasse norm theorem Artinreciprocity Local class field theory Iwasawa theory Herbrand–Ribet theorem Vandiver's...
In mathematics, the Weil reciprocity law is a result of André Weil holding in the function field K(C) of an algebraic curve C over an algebraically closed...
Archimedes. Artinreciprocity law is a general theorem in number theory that forms a central part of global class field theory. Named after Emil Artin. Ashby's...
/ 2. {\displaystyle \epsilon (x)=(x-1)/2.} Rational reciprocity law Neukirch (1999) p.335 Artin, E.; Hasse, H. (1928), "Die beiden Ergänzungssätze zum...
accounted for by class field theory: their L-functions are Artin L-functions, as Artinreciprocity shows. But even a field as simple as the Gaussian field...
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