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On p-adic analytic continuation with applications to generating elements

Part of: Algebraic number theory: local and $p$-adic fields

Published online by Cambridge University Press:  10 June 2015

Victor Alexandru ,
Marian Vâjâitu  and
Alexandru Zaharescu
Victor Alexandru
Affiliation:
Department of Mathematics, University of Bucharest, 14 Academiei Street, 010014 Bucharest, Romania
Marian Vâjâitu
Affiliation:
Simion Stoilow Institute of Mathematics of the Romanian Academy, Research Unit 5, PO Box 1-764, 014700 Bucharest, Romania ([email protected])
Alexandru Zaharescu
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Altgeld Hall, 1409 W Green Street, Urbana, IL 61801, USA
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Abstract

Given a prime number p and the Galois orbit O(T) of an integral transcendental element T of , the topological completion of the algebraic closure of the field of p-adic numbers, we study the p-adic analytic continuation around O(T) of functions defined by limits of sequences of restricted power series with p-adic integer coefficients. We also investigate applications to generating elements for or for some classes of closed subfields of .

Keywords

p-adic analytic functionslocal fieldsgenerating elements

MSC classification

Secondary: 11S99: None of the above, but in this section
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 1 , February 2016 , pp. 1 - 10
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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