Submission date: 28 July 2020

Abstract:

We axiomatize a class of existentially closed exponential fields equipped with an E-derivation. We apply our results to the field of real numbers endowed with exp(x) the classical exponential function defined by its power series expansion and to the field of p-adic numbers endowed with the function exp(px) defined on the p-adic integers where p is a prime number strictly bigger than 2 (or with exp(4x) when p=2).

Mathematics Subject Classification: 03C60, 03C10, 12L12, 12H05

Keywords and phrases:

Full text arXiv 2007.14344: pdf, ps.