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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On natural radii of $ p$-adic convergence


Authors: B. Dwork and P. Robba
Journal: Trans. Amer. Math. Soc. 256 (1979), 199-213
MSC: Primary 12B40; Secondary 34A25
MathSciNet review: 546915
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Abstract: We study the radius of p-adic convergence of power series which represent algebraic functions. We apply the p-adic theory of ordinary linear differential equations to show that the radius of convergence is the natural one, provided the degree of the function is less than p. The study of similar questions for solutions of linear differential equations is indicated.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0546915-9
Keywords: Differential equation, radius of convergence, p-adic
Article copyright: © Copyright 1979 American Mathematical Society