On λ-invariants attached to cyclic cubic number fields

Delbourgo, Daniel; Qin, Chao

On λ-invariants attached to cyclic cubic number fields

dc.contributor.author	Delbourgo, Daniel	en_NZ
dc.contributor.author	Qin, Chao	en_NZ
dc.date.accessioned	2016-01-13T03:52:29Z
dc.date.available	2015	en_NZ
dc.date.available	2016-01-13T03:52:29Z
dc.date.issued	2015	en_NZ
dc.description.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.
dc.format.mimetype	application/pdf
dc.identifier.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	en
dc.identifier.doi	10.1112/S1461157015000224	en_NZ
dc.identifier.issn	1461-1570	en_NZ
dc.identifier.uri	https://hdl.handle.net/10289/9843
dc.language.iso	en
dc.publisher	London Mathematical Society	en_NZ
dc.relation.isPartOf	LMS Journal of Computation and Mathematics	en_NZ
dc.rights	© 2015 Authors.
dc.title	On λ-invariants attached to cyclic cubic number fields	en_NZ
dc.type	Journal Article
pubs.begin-page	684
pubs.elements-id	136028
pubs.end-page	698
pubs.issue	1	en_NZ
pubs.organisational-group	/Waikato
pubs.organisational-group	/Waikato/FCMS
pubs.organisational-group	/Waikato/FCMS/Mathematics
pubs.organisational-group	/Waikato/Student
pubs.publication-status	Published	en_NZ
pubs.volume	18	en_NZ