- Minkowski's bound
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In algebraic number theory, Minkowski's bound gives an upper bound of the norm of ideals to be checked in order to determine the class number of a number field K. It is named for the mathematician Hermann Minkowski.
Let D be the discriminant of the field, n be the degree of K over , and 2r2 = n − r1 be the number of complex embeddings where r1 is the number of real embeddings. Then every class in the ideal class group of K contains an integral ideal of norm not exceeding Minkowski's bound
In particular, the class group is generated by the prime ideals of norm at most MK.
The result is a consequence of Minkowski's theorem.
References
- Using Minkowski's Constant To Find A Class Number on PlanetMath
- Lang, Serge (1994). Algebraic Number Theory (second edition ed.). New York: Springer. ISBN 0387942254.
- Stevenhagen, Peter. Number Rings.
- The Minkowski Bound at Secret Blogging Seminar
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