Inductive construction of the p-adic zeta functions for non-commutative p-extensions of totally real fields with exponent p

  title={Inductive construction of the p-adic zeta functions for non-commutative p-extensions of totally real fields with exponent p},
  author={Takashi Hara},
  journal={arXiv: Number Theory},
  • T. Hara
  • Published 15 August 2009
  • Mathematics
  • arXiv: Number Theory
We construct the p-adic zeta function for a one-dimensional (as a p-adic Lie extension) non-commutative p-extension of a totally real number field such that the finite part of its Galois group is a pgroup with exponent p. We first calculate the Whitehead groups of the Iwasawa algebra and its canonical Ore localisation by using Oliver-Taylor's theory upon integral logarithms. This calculation reduces the existence of the non-commutative p-adic zeta function to certain congruence conditions among… 
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