by Popescu, Nicolae; Vâjâitu, Marian; Zaharescu, Alexandru

Let T be a transcendental element of
% MathType!Translator!2!1!AMS LaTeX.tdl!TeX — AMS-LaTeX!
% MathType!MTEF!2!1!+-
% feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
% garmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wz
% aebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq
% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq
% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaeaaakeaacq
% WIceYOdaWgaaWcbaGaamiCaaqabaaaaa!3A08!$$\mathbb{C}_p
$$ and
% MathType!Translator!2!1!AMS LaTeX.tdl!TeX — AMS-LaTeX!
% MathType!MTEF!2!1!+-
% feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
% garmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wz
% aebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq
% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq
% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaeaaakeaaca
% qGpbWaaeWaaeaacaWGubaacaGLOaGaayzkaaGaeyypa0ZaaiWaaeaa
% cqaHdpWCdaqadaqaaiaadsfaaiaawIcacaGLPaaacaGG6aGaeq4Wdm
% NaeyicI4Saae4raiaabggacaqGSbWaaSbaaSqaaiaabogacaqGVbGa
% aeOBaiaabshaaeqaaOWaaeWaaeaadaWcgaqaaiablkqiJoaaBaaale
% aacaWGWbaabeaaaOqaaiablQriKoaaBaaaleaacaWGWbaabeaaaaaa
% kiaawIcacaGLPaaaaiaawUhacaGL9baaaaa!5374!
$$
{\text{O}}{\left( T \right)} = {\left\{ {\sigma {\left( T \right)}:\sigma \in {\text{Gal}}_{{{\text{cont}}}} {\left( {{\mathbb{C}_{p} } \mathord{\left/
{\vphantom {{\mathbb{C}_{p} } {\mathbb{Q}_{p} }}} \right.
\kern-\nulldelimiterspace} {\mathbb{Q}_{p} }} \right)}} \right\}}
$$ the orbit of T. On
% MathType!Translator!2!1!AMS LaTeX.tdl!TeX — AMS-LaTeX!
% MathType!MTEF!2!1!+-
% feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
% garmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wz
% aebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq
% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq
% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaeaaakeaaca
% qGpbWaaeWaaeaacaWGubaacaGLOaGaayzkaaaaaa!3AC4!
$$
{\text{O}}{\left( T \right)}
$$we have a Haar measure
% MathType!Translator!2!1!AMS LaTeX.tdl!TeX — AMS-LaTeX!
% MathType!MTEF!2!1!+-
% feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
% garmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wz
% aebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq
% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq
% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaeaaakeaacq
% aHapaCdaqadaqaaiaadsfaaiaawIcacaGLPaaaaaa!3BAF!$$\pi \left( T \right)$$. The goal of this paper is to characterize all the elements of
% MathType!Translator!2!1!AMS LaTeX.tdl!TeX — AMS-LaTeX!
% MathType!MTEF!2!1!+-
% feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
% garmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wz
% aebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq
% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq
% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaeaaakeaacq
% WIceYOdaWgaaWcbaGaamiCaaqabaaaaa!3A08!$$\mathbb{C}_p$$ for which the integral
% MathType!Translator!2!1!AMS LaTeX.tdl!TeX — AMS-LaTeX!
% MathType!MTEF!2!1!+-
% feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX
% garmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy0Hgip5wz
% aebbnrfifHhDYfgasaacH8qrps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq
% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq
% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaeaaakeaaca
% qGubGaaeOCamaabmaabaGaamivaaGaayjkaiaawMcaaiaacQdacqGH
% 9aqpdaWdXaqaaiaadQhacaqGKbGaeqiWda3aaSbaaSqaaiaadshaae
% qaaOWaaeWaaeaacaWG6baacaGLOaGaayzkaaaaleaacaqGpbWaaeWa
% aeaacaWGubaacaGLOaGaayzkaaaabaaaniabgUIiYdaaaa!4A39!
$$
{\text{Tr}}{\left( T \right)}: = {\int_{{\text{O}}{\left( T \right)}}^{} {z{\text{d}}\pi _{t} {\left( z \right)}} }
$$, called the trace of T, is well defined.

DOI: 10.1007/s10468-005-9003-0
Online Date: 4/19/2006
Print publication date: 2/1/2006
View article on SpringerLink