Related papers: Two conjectures on integer arithmetic and their ap…
This paper has been withdrawn by the authors because M. Aschenbrenner pointed out that the proof of theorem 3.1 was incorrect.
This paper has been withdrawn by the author. The conjecture follows from the finiteness of group von Neumann algebras.
This paper has been withdrawn by the author due to a crucial error in equation (51).
This paper has been withdrawn by the author due to some errors.
We first propose two conjectural estimates on Diophantine approximation of logarithms of algebraic numbers. Next we discuss the state of the art and we give further partial results on this topic.
This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.
The paper has benn withdrawn because the computation of the external virial contains an error which invalidate the main result.
We collect a number of open questions concerning Diophantine equations, Diophantine Approximation and transcendental numbers. Revised version: corrected typos and added references.
This paper has been withdrawn by the author because Proposition 1 is not valid.
This paper has been withdrawn by the author due to a crucial error in the proof of Theorem 1.
This paper has been withdrawn by the authors, because it has been made obsolete by the detailed expositions in our papers in arXiv:0812.4885 (the mathematics part) and arXiv:0812.4737 (the economics part).
We show that some mathematical results and their negations are both deducible. The derived contradictions indicate the inconsistency of current mathematics. This paper is an updated version of arXiv:math/0606635v3 with additional results…
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
This paper has been withdrawn by the author due to a mistake in the proof of the main theorem.
The paper has been withdrawn by the author, due to it being fundamentally flawed. The author apologizes for any inconvenience it may have caused.
This paper has been withdrawn by the author due to a crucial error.
An elementary gap in the proof of corollary 2.2 was found, the claim in the first version of the paper is thus retracted.
This paper has been withdrawn by the author due to a crucial error in the formulation.
This paper has been withdrawn by the author due to the presented idea is wrong.
This paper is cancelled