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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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Article copyright: © Copyright 1992 American Mathematical Society

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