# Inductive construction of the p-adic zeta functions for non-commutative p-extensions of totally real fields with exponent p - Mathematics > Number Theory

Inductive construction of the p-adic zeta functions for non-commutative p-extensions of totally real fields with exponent p - Mathematics > Number Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: We construct the p-adic zeta function for a one-dimensional as a p-adic Lieextension non-commutative p-extension of a totally real number field such thatthe finite part of its Galois group is a pgroup with exponent p. We firstcalculate the Whitehead groups of the Iwasawa algebra and its canonical Orelocalisation by using Oliver-Taylor-s theory upon integral logarithms. Thiscalculation reduces the existence of the non-commutative p-adic zeta functionto certain congruence conditions among abelian p-adic zeta pseudomeasures. Thenwe finally verify these congruences by using Deligne-Ribet-s theory and certaininductive technique. As an application we shall prove a special case of thep-part of the non-commutative equivariant Tamagawa number conjecture forcritical Tate motives. The main results of this paper give generalisation ofthose of the preceding paper of the author.

Author: ** Takashi Hara**

Source: https://arxiv.org/