Radii of convergence and index for 𝑝-adic differential operators

Young, Paul Thomas

doi:10.1090/S0002-9947-1992-1066451-X

Radii of convergence and index for $p$-adic differential operators
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Trans. Amer. Math. Soc. 333 (1992), 769-785 Request permission

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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On the index of

adic differential operators

Application to twisted exponential sums

119-120

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