Non-archimedean analysis on the extended hyperreal line *R_d and some transcendence conjectures over field Q and *Q_ω

Details Non-archimedean analysis on the extended hyperreal line *R_d and some transcendence conjectures over field Q and *Q_ω Non-archimedean analysis on the extended hyperreal line *R_d and some transcendence conjectures over field Q and *Q_ω

2009-07-02

arxiv.org/abs/0907.0467v4

Mathematics

General Mathematics

190p

Scientific paper

In this paper possible completion *R_d of the Robinson non-archimedean field *R constructed by Dedekind sections. As interesting example I show how, a few simple ideas from non-archimedean analysis on the pseudo-ring *R_d gives a short clear nonstandard reconstruction for the Euler's original proof of the Goldbach-Euler theorem. Given an analytic function of one complex variable $f \in C[z]$,we investigate the arithmetic nature of the values of f at transcendental points.

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