TY - JOUR

T1 - Growth of solutions of linear differential equations at a logarithmic singularity

AU - Adolphson, A.

AU - Dwork, B.

AU - Sperber, S.

PY - 1982/5

Y1 - 1982/5

N2 - 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.

AB - 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.

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U2 - 10.1090/S0002-9947-1982-0648090-9

DO - 10.1090/S0002-9947-1982-0648090-9

M3 - Article

AN - SCOPUS:0013306150

SN - 0002-9947

VL - 271

SP - 245

EP - 252

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 1

ER -