The Hurwitz Product, p-Adic Topology on ℤ, and Fundamental Solution to Linear Differential Equation in the Ring ℤ[[x]]
- Authors: Gefter S.L.1, Goncharuk A.B.1
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Affiliations:
- Karazin Kharkiv National University
- Issue: Vol 228, No 6 (2018)
- Pages: 633-638
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/240328
- DOI: https://doi.org/10.1007/s10958-017-3651-6
- ID: 240328
Cite item
Abstract
We study the linear inhomogeneous first order differential equation by′ + f(x) = y in the ring of formal power series with integer coefficients. Using the p-adic topology on the ring of integers, we construct a counterpart of the Hurwitz product of the Euler series and an arbitrary formal power series with integer coefficients. It is shown that the Euler series can be interpreted as the fundamental solution to the equation under consideration. Bibliography: 8 titles.
About the authors
S. L. Gefter
Karazin Kharkiv National University
Author for correspondence.
Email: gefter@univer.kharkov.ua
Ukraine, 4, pl. Svobody, Kharkiv, 61000
A. B. Goncharuk
Karazin Kharkiv National University
Email: gefter@univer.kharkov.ua
Ukraine, 4, pl. Svobody, Kharkiv, 61000