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Cyclotomic Invariant


Let p be an odd prime and F_n the cyclotomic field of p^(n+1)th roots of unity over the rational field. Now let p^(e(n)) be the power of p which divides the class number h_n of F_n. Then there exist integers mu_p,lambda_p>=0 and nu_p such that

 e(n)=mu_pp^n+lambda_pn+nu_p

for all sufficiently large n. For regular primes, mu_p=lambda_p=nu_p=0.


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References

Johnson, W. "Irregular Primes and Cyclotomic Invariants." Math. Comput. 29, 113-120, 1975.

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Cyclotomic Invariant

Cite this as:

Weisstein, Eric W. "Cyclotomic Invariant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CyclotomicInvariant.html

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