Other functions: subcycloiwasawa
subcycloiwasawa(fH, p); let p be a prime, F∞ the cyclotomic Zp-extension of F and let
Fn be its n-th layer. Computes the λ-invariant attached to F∞
subcycloiwasawa(fH, p, k) compute the Iwasawa polynomial (of degree λ) modulo
pk−logp λ
.
Not all cases are implemented in this function; e.g., p must be odd and not divide [F : Q] unless
F is quadratic. For quadratic fields, more information is actually output about the behaviour of AF
along F∞:
? subcycloiwasawa(x^2 + 1501391, 3)
time = 28 ms.
%22 = [14, -16, [2, 5]]
This says that at p = 3, we have λ = 14 and that e0 = 2, e1 = 5 and en = 14n − 16 for all
n > 2, where 3en is the 3-part of the class number of Fn.
Atelier 2022 (13/01/2022) – p. 13/13