An application of newton iteration procedure to $p$-adic differential equations

Yasutaka Sibuya

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On Morita’s $p$ -adic $Γ$ -function

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Poles of $p$ -adic complex powers and Newton polyhedra

Jan Denef (1984-1985)

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A note on the $p$ -adic gamma function

Bernard Dwork (1981-1982)

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On the $p$ -adic continuation of the logarithmic derivative of certain hypergeometric functions

Steven Sperber, Yasutaka Sibuya (1984-1985)

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On generalized $p$ -adic integration

Arnt Volkenborn (1974)

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The Gross-Koblitz formula revisited

Alain M. Robert (2001)

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Bounds on the radius of the p-adic Mandelbrot set

Jacqueline Anderson (2013)

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Let $f (z) = z^{d} + a_{d - 1} z^{d - 1} + . . . + a_{1} z \in ℂ_{p} [z]$ be a degree d polynomial. We say f is post-critically bounded, or PCB, if all of its critical points have bounded orbit under iteration of f. It is known that if p ≥ d and f is PCB, then all critical points of f have p-adic absolute value less than or equal to 1. We give a similar result for 1/2d ≤ p < d. We also explore a one-parameter family of cubic polynomials over ℚ₂ to illustrate that the p-adic Mandelbrot set can be quite complicated when p < d, in contrast with the...

Relaxed algorithms for $p$ -adic numbers

Jérémy Berthomieu, Joris van der Hoeven, Grégoire Lecerf (2011)

Journal de Théorie des Nombres de Bordeaux

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Current implementations of $p$ -adic numbers usually rely on so called zealous algorithms, which compute with truncated $p$ -adic expansions at a precision that can be specified by the user. In combination with Newton-Hensel type lifting techniques, zealous algorithms can be made very efficient from an asymptotic point of view. In the similar context of formal power series, another so called lazy technique is also frequently implemented....

Puiseux expansions

Bernard M. Dwork (1982-1983)

Groupe de travail d'analyse ultramétrique

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Displaying similar documents to “An application of newton iteration procedure to p -adic differential equations”

Displaying similar documents to “An application of newton iteration procedure to $p$ -adic differential equations”