Growth of solutions of linear differential equations at a logarithmic singularity

A. Adolphson, B. Dwork, S. Sperber

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We consider differential equations Y' = AY with a regular singular point at the origin, where A is an n X n matrix whose entries are p-adic meromorphic functions. If the solution matrix at the origin is of the form Y — P exp(θ log x), where P is an n X n matrix of meromorphic functions and θ is an n X n constant matrix whose Jordan normal form consists of a single block, then we prove that the entries of P have logarithmic growth of order n — 1.

Original languageEnglish (US)
Pages (from-to)245-252
Number of pages8
JournalTransactions of the American Mathematical Society
Volume271
Issue number1
DOIs
StatePublished - May 1982

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