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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Effective $p$-adic bounds for solutions of homogeneous linear differential equations
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by B. Dwork and P. Robba PDF
Trans. Amer. Math. Soc. 259 (1980), 559-577 Request permission


We consider a finite set of power series in one variable with coefficients in a field of characteristic zero having a chosen nonarchimedean valuation. We study the growth of these series near the boundary of their common “open” disk of convergence. Our results are definitive when the wronskian is bounded. The main application involves local solutions of ordinary linear differential equations with analytic coefficients. The effective determination of the common radius of convergence remains open (and is not treated here).
    P. Deligne, Équations différentielles à points singuliers réguliers, Lecture Notes in Math., vol. 163, Springer, Berlin and New York, 1970.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 259 (1980), 559-577
  • MSC: Primary 12B40; Secondary 14G20
  • DOI:
  • MathSciNet review: 567097