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LIPSCHITZIAN ELEMENTS OVER p-ADIC FIELDS

Published online by Cambridge University Press:  27 July 2005

ALEXANDRU ZAHARESCU
ALEXANDRU ZAHARESCU
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL, 61801, USA e-mail: zaharesc@math.uiuc.edu
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Abstract

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Let $p$ be a prime number, $\Q_p$ the field of $p$-adic numbers, $K$ a finite field extension of $\Q_p$, $\skew4\bar K$ a fixed algebraic closure of $K$, and $\C_p$ the completion of $\skew4\bar K$ with respect to the $p$-adic valuation. We discuss some properties of Lipschitzian elements, which are elements $T$ of $\C_p$ defined by a certain metric condition that allows one to integrate Lipschitzian functions along the Galois orbit of $T$ over $K$ with respect to the Haar distribution.

Keywords

11S99
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 47 , Issue 2 , May 2005 , pp. 363 - 372
Copyright
2005 Glasgow Mathematical Journal Trust