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

 

An index theorem for $ p$-adic differential operators


Author: A. Adolphson
Journal: Trans. Amer. Math. Soc. 216 (1976), 279-293
MSC: Primary 14G99; Secondary 12B99, 34A30
MathSciNet review: 0387284
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Abstract: A system of first order linear differential operators satisfying conditions arising naturally in geometry (rational function coefficients, regular singularities, non-Liouville exponents) is considered. It is shown that the index of the system on certain spaces of holomorphic functions can be calculated by restricting to a subspace of rational functions. This is applied to obtain an explicit formula for the index of a single kth order linear differential operator.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0387284-4
PII: S 0002-9947(1976)0387284-4
Keywords: p-adic numbers, index, regular singularity, Mittag-Leffler Theorem
Article copyright: © Copyright 1976 American Mathematical Society