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Abstract
We describe an algorithm for finding the coefficients of F(X) modulo powers of p, where p ≠2 is a prime number and F(X) is the power series associated to the zeta function of Kubota and Leopoldt. We next calculate the 5-adic and 7-adic λ-invariants attached to those cubic extensions K/Q with cyclic Galois group A₃ (up to field discriminant <10⁷), and also tabulate the class number of K(e2πi/p) for p=5 and p=7. If the λ-invariant is greater than zero, we then determine all the zeros for the corresponding branches of the p-adic L-function and deduce Λ-monogeneity for the class group tower over the cyclotomic Zp-extension of K.
Type
Journal Article
Type of thesis
Series
Citation
Delbourgo, D., & Qin, C. (2015). On λ-invariants attached to cyclic cubic number fields. LMS Journal of Computation and Mathematics, 18(1), 684–698. http://doi.org/10.1112/S1461157015000224
Date
2015
Publisher
London Mathematical Society
Degree
Supervisors
Rights
© 2015 Authors.