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2013 The logarithmic growth of element of Robba ring which satisfies Frobenius equation over bounded Robba ring
Takahiro Nakagawa
Tohoku Math. J. (2) 65(2): 179-198 (2013). DOI: 10.2748/tmj/1372182721

Abstract

We study the logarithmic growth of an element of the Robba ring which satisfies a Frobenius equation over the bounded Robba ring. Chiarellotto and Tsuzuki computed the logarithmic growth of analytic functions on the open unit disc with coefficients in a $p$-adic local field which satisfy Frobenius equations over bounded functions of rank 2. We extend their result by replacing those functions by elements of the Robba ring which satisfy Frobenius equations over the bounded Robba ring. Moreover, we will see, in special cases, the zeros of these functions have some cyclicity and the logarithmic growth can be computed by the zeros of these function.

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Takahiro Nakagawa. "The logarithmic growth of element of Robba ring which satisfies Frobenius equation over bounded Robba ring." Tohoku Math. J. (2) 65 (2) 179 - 198, 2013. https://doi.org/10.2748/tmj/1372182721

Information

Published: 2013
First available in Project Euclid: 25 June 2013

zbMATH: 1297.12001
MathSciNet: MR3079284
Digital Object Identifier: 10.2748/tmj/1372182721

Subjects:
Primary: 12H25

Rights: Copyright © 2013 Tohoku University

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Vol.65 • No. 2 • 2013
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