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      On λ-invariants attached to cyclic cubic number fields

      Delbourgo, Daniel; Qin, Chao
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      LambdaCubicFinal.pdf
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      DOI
       10.1112/S1461157015000224
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      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
      Permanent Research Commons link: https://hdl.handle.net/10289/9843
      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.
      Date
      2015
      Type
      Journal Article
      Publisher
      London Mathematical Society
      Rights
      © 2015 Authors.
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      • Computing and Mathematical Sciences Papers [1455]
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