相关论文: On the Koszul Betti numbers in positive characteri…

This paper has been withdrawn by the author(s), due a mistake of factor 1/2.

The paper was withdrawn by the author. Further research is needed.

This paper has been withdrawn by the author because there are some typos in proofs.

Paper withdrawn by the author after learning that its main conclusion was given earlier in a slightly different language in Appendix D of A. J. Buras, R. Fleischer, S. Recksiegel, and F.Schwab, hep-ph/0402112.

An elementary gap in the proof of corollary 2.2 was found, the claim in the first version of the paper is thus retracted.

There is a conceptual error in the main argument of this paper (essentially a regularization scheme is changed in the middle of a calculation), and therefore it is withdrawn. Interested readers are instead referred to hep-th/9811137.

This paper has been withdrawn by the author. The main result is wrong, as M.Matignon and C. Lehr provided a counterexample to it.

This paper has been withdrawn due a crucial mistake due to a crucial mistake in the proof of Lemma 2.3.

This paper was withdrawn by the authors. The mistake in math.AG/0209223 affects also this paper.

This paper has been withdrawn by the author due to the incorrect argument for the security.

This paper has been removed by the author due to a misstatement in Theorem 1 and a gap in its proof. A corrected and largely extended successor (a joint work with Thomas Bauer and Tomasz Szemberg) can be found under math.AG/0312211,

The author decided to withdraw this paper by 1) an error in Lemma 5.11 (and 5.12) which requires some justification; 2) the main result of this paper suffers overlap with arXiv:1203.5254; 3) the author decided to split arXiv:1203.5254 into…

This paper has been withdrawn due to a critical error discovered in Theorem 4.21. Anyone with a historical or pragamatic interest in prior "negative results", however - e.g., failed proof attempts relating to the (in)consistency of ZF or…

The paper is withdrawn by the author due to a recently discovered flaw in a basic proof.

The paper has been withdrawn because the research work is still in progress.

The paper is withdrawn.

This paper has been withdrawn by the author due to a crucial error in the submission action.

This paper has been withdrawn by the author due to serious flaws in certain proofs. For instance, the method used to construct certain automorphic representations is flawed.

Paper has been withdrawn due to an error in the basic argument that the states corresponding to the zeros of Riemann Zeta with Re[s]<1/2 allow a Fourier expansion in the basis provided by the states having Re[s]>= 1/2.

This paper has been withdrawn due to non-clearness of some technical points, as well as lack of a reasonable statement of quantization conjecture.