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On the Existence of Trace for Elements of \mathbb{C}_p

Authors:	Nicolae Popescu Marian Vâjâitu Alexandru Zaharescu

Institution:	(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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