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 $\mu_p, \lambda_p\geq 0$ and $\nu_p$ such that

$$e(n)=\mu_p p^n+\lambda_p n+\nu_p$$

for all sufficiently large $n$. For Regular Primes, $\mu_p=\lambda_p=\nu_p=0$.

References

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