Local p-Adic Differential Equations

Marius van der Put, Lenny Taelman

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    Abstract

    This paper studies divergence in solutions of p-adic linear local differential equations. Such divergence is related to the notion of p-adic Liouville numbers. Also, the influence of the divergence on the differential Galois groups of such differential equations is explored. A complete result is given for second order equations and a conjecture for higher order equations is proposed.
    Original languageEnglish
    Title of host publicationp-adic mathematical physics
    Subtitle of host publication2nd international conference, Belgrade, Serbia and Montenegro, 15-21 September, 2005
    EditorsA Yu Khrennikov, Z. Rakic, I.V. Volovich
    Place of PublicationNew York
    PublisherAIP PRESS
    Pages291-297
    Number of pages7
    ISBN (Electronic) 9780735403185
    Publication statusPublished - 2005
    Event2nd International Conference on p-Adic Mathematical Physics - Belgrade, Serbia
    Duration: 15-Sep-200521-Sep-2005

    Publication series

    NameAIP conference proceedings
    PublisherAIP
    Volume826

    Conference

    Conference2nd International Conference on p-Adic Mathematical Physics
    Country/TerritorySerbia
    CityBelgrade
    Period15/09/200521/09/2005

    Keywords

    • divergence
    • Liouville numbers
    • differential equations
    • p-adic analysis

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