Chebotarev density theorem

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In mathematics, specifically in algebraic number theory, the Chebotarev density theorem, named after Nikolai Chebotarev, statistically describes the splitting of primes in a given Galois extension K {\displaystyle K} of the field Q {\displaystyle \mathbb {Q} } of rational numbers. Generally speaking, a prime integer will factor into several ideal primes in the ring of algebraic integers of K {\displaystyle K} . There are only finitely many patterns of splitting that may occur. Although the full description of the splitting of every prime p {\displaystyle p} in a general Galois extension is a major unsolved problem, the Chebotarev density theorem says that the frequency of the occurrence of a given pattern, for all primes p {\displaystyle p} less than a...

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