The ordered pair 
,
where 
is the number of real embeddings of the number
field and 
is the number of complex conjugate pairs of
imaginary embeddings. The extension
field degree of the number field is 
.
Number Field Signature
See also
Field Embedding, Fundamental Unit, Imaginary Embedding, Number Field, Real Embedding, UnitThis entry contributed by Kevin O'Bryant
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References
Cohen, H. A Course in Computational Algebraic Number Theory, 3rd. corr. ed. New York: Springer-Verlag, 1996.Referenced on Wolfram|Alpha
Number Field SignatureCite this as:
O'Bryant, Kevin. "Number Field Signature." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/NumberFieldSignature.html