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Transactions of the American Mathematical Society

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Effective $p$-adic bounds for solutions of homogeneous linear differential equations

Authors: B. Dwork and P. Robba
Journal: Trans. Amer. Math. Soc. 259 (1980), 559-577
MSC: Primary 12B40; Secondary 14G20
MathSciNet review: 567097
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Abstract: We consider a finite set of power series in one variable with coefficients in a field of characteristic zero having a chosen nonarchimedean valuation. We study the growth of these series near the boundary of their common “open” disk of convergence. Our results are definitive when the wronskian is bounded. The main application involves local solutions of ordinary linear differential equations with analytic coefficients. The effective determination of the common radius of convergence remains open (and is not treated here).

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Article copyright: © Copyright 1980 American Mathematical Society