Related papers: Two conjectures on integer arithmetic and their ap…
The paper is withdrawn.
We show that Artin's conjecture concerning p-adic solubility of Diophantine equations fails for infinitely many systems of r homogeneous diagonal equations whenever r>1.
This paper has been withdrawn due to an error, and no further revisions will be made.
This paper has been withdrawn due to non-clearness of some technical points, as well as lack of a reasonable statement of quantization conjecture.
The present work includes some of the author's original researches on integer solutions of Diophantine liner equations and systems. The notion of "general integer solution" of a Diophantine linear equation with two unknowns is extended to…
This paper has been withdrawn by the author because there are some typos in proofs.
This paper has been withdrawn by the author, due an error in claim 1.
This paper has been withdrawn by the author, due to an error in the proof of lemma 7.4. However, numerical evidence strongly suggest that this lemma is true.
Let f(1)=1, and let f(n+1)=2^{2^{f(n)}} for every positive integer n. We conjecture that if a system S \subseteq {x_i \cdot x_j=x_k: i,j,k \in {1,...,n}} \cup {x_i+1=x_k: i,k \in {1,...,n}} has only finitely many solutions in non-negative…
The methods used to prove the main result must be incorrect, as they can be used to arrive at a contradiction with previously known results. Thus the paper was withdrawn.
This paper has been withdrawn due to a crucial theoretical error.
This paper has been withdrawn by the author due to some error in the result
It is shown that the arguments in the reply of Z.-D. Zhang (arXiv:0812.0194) to the comment arXiv:0811.1802 defending his conjectures in arXiv:0705.1045 are invalid. His conjectures have been thoroughly disproved.
This paper has been withdrawn by the author, due to an error in the proof of Theorem 3.8.
This paper has been withdrawn by the authors because it has been combined with "Higher Auslander Algebras Admitting Trivial Maximal Orthogonal Subcategories" (arXiv:0903.0761) together. Please see the new version of the latter paper for the…
We survey classical and recent results on exponents of Diophantine approximation. We give only a few proofs and highlight several open problems.
This paper has been withdrawn by the authors due to an error in Section 7.
In this paper we adopt a geometric point of view regarding a famous conjecture due to Littlewood in diophantine approximation of real numbers. Following the spirit of the geometric theory of continued fractions, we give a sufficient…
This paper has been withdrawn by the authors due to a mistake in the proof of Theorem 1.
This paper has been withdrawn by the author due to incomplete interpretation for the results.