p-adic exponential ring, p-adic Schanuel's conjecture and decidability
Logic
2014-08-06 v1
Abstract
Let exp(x) be the function determined by the classical power series of the exponentiation. Then E_p(x):=exp(px) is well-defined on Zp, the ring of p-adic integer (for p not equal to 2, we set E_2(x)=exp(4x)). Furthermore, E_p determines a structure of exponential ring on Zp. In this paper, we prove that if a p-adic version of Schanuel's conjecture is true then the theory of (Zp, +, ., 0, 1, E_p) is decidable.
Keywords
Cite
@article{arxiv.1408.0900,
title = {p-adic exponential ring, p-adic Schanuel's conjecture and decidability},
author = {Nathanaël Mariaule},
journal= {arXiv preprint arXiv:1408.0900},
year = {2014}
}