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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Radii of convergence and index for $ p$-adic differential operators


Author: Paul Thomas Young
Journal: Trans. Amer. Math. Soc. 333 (1992), 769-785
MSC: Primary 12H25; Secondary 11S80
MathSciNet review: 1066451
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Abstract: We study the radii of $ p$-adic convergence of solutions at a generic point of homogeneous linear differential operators whose coefficients are analytic elements. As an application we prove a conjecture of P. Robba (for a certain class of operators) concerning the relation between radii of convergence and index on analytic elements. We also give an explicit factorization theorem for $ p$-adic differential operators, based on the radii of generic convergence and the slopes of the associated Newton polygon.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1066451-X
PII: S 0002-9947(1992)1066451-X
Article copyright: © Copyright 1992 American Mathematical Society



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