On {\pi}-exponentials II : Closed formula for the index
Abstract
(Quoted from the article) This article pursue the series, initiated by [Ric14], dedicated to Pulita's {\pi}-exponentials and p-adic differential equation of rank one with coefficients a polynomial in a ultrametric extension of the field of -adic numbers. We complement [Ric14] with a closed formula for the index. The "-typical" particular case answers one problem studied in [Mor10]. We also answer a question [Rob86, {\S}2.4] of Robba on the comparison from rational cohomology toward Dwork cohomology. We even indicate a procedure to palliate the lack of isomorphy of this comparison. We establish by the way a characterisation of soluble equations up to equivalence on the dagger algebra. An appendix determine the polynomial complexity of the derived algorithm.
Cite
@article{arxiv.1403.0615,
title = {On {\pi}-exponentials II : Closed formula for the index},
author = {Rodolphe Richard},
journal= {arXiv preprint arXiv:1403.0615},
year = {2017}
}