On log-growth of solutions of -adic differential equations with -adic exponents

  • Takahiro Nakagawa

    Chiba University, Japan
On log-growth of solutions of $p$-adic differential equations with $p$-adic exponents cover

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Abstract

We consider a differential system , where is a matrix whose coefficients are power series which converge and are bounded on the open unit disc . Assume that is a diagonal matrix with -adic integer coefficients. Then there exists a solution matrix of the form at if all differences of exponents of the system are -adically non-Liouville numbers. We give an example where is analytic on the -adic open unit disc and has log-growth greater than . Under some conditions, we prove that if a solution matrix at a generic point has log-growth , then has log-growth .

Cite this article

Takahiro Nakagawa, On log-growth of solutions of -adic differential equations with -adic exponents. Rend. Sem. Mat. Univ. Padova 147 (2022), pp. 153–168

DOI 10.4171/RSMUP/95