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Artin reciprocity law
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Artin reciprocity law
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
. 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
.
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