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On the Existence of Trace for Elements of mathbb{C}_p
Authors:Nicolae Popescu  Marian Vâjâitu  Alexandru Zaharescu
Affiliation:(1) Institute of Mathematics of the Romanian Academy, PO Box 1-764, Bucharest, 70700, Romania;(2) Department of Mathematics, University of Illinois at Urbana-Champaign, Altgeld Hall, 1409 W. Green Street, Urbana, IL, 61801, U.S.A.
Abstract:Let T be a transcendental element of$$mathbb{C}_p 
$$ and$$
{text{O}}{left( T right)} = {left{ {sigma {left( T right)}:sigma  in {text{Gal}}_{{{text{cont}}}} {left( {{mathbb{C}_{p} } mathord{left/
 {vphantom {{mathbb{C}_{p} } {mathbb{Q}_{p} }}} right.
 kern-nulldelimiterspace} {mathbb{Q}_{p} }} right)}} right}}
$$ the orbit of T. On$$
{text{O}}{left( T right)}
$$we have a Haar measure$$pi left( T right)$$. The goal of this paper is to characterize all the elements of$$mathbb{C}_p$$ for which the integral$$
{text{Tr}}{left( T right)}: = {int_{{text{O}}{left( T right)}}^{} {z{text{d}}pi _{t} {left( z right)}} }
$$, called the trace of T, is well defined.Presented by A. Verschoren
Keywords:11S99
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